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Volume 117, Number 1, January, 2010Anonymous Front Matter . . . . . . . . . . . . . . ?? Aaron Abrams and Skip Garibaldi Finding Good Bets in the Lottery, and Why You Shouldn't Take Them . . . . . . 3--26 Deborah E. Berg and Serguei Norine and Francis Edward Su and Robin Thomas and Paul Wollan Voting in Agreeable Societies . . . . . 27--39 Christopher S. Hardin Agreement in Circular Societies . . . . 40--49 Barry Lewis Revisiting the Pascal Matrix . . . . . . 50--66 Mircea I. C\^\irnu Newton's Identities and the Laplace Transform . . . . . . . . . . . . . . . 67--71 Kurt Girstmair Farey Sums and Dedekind Sums . . . . . . 72--78 Friedrich Pillichshammer Euler's Constant and Averages of Fractional Parts . . . . . . . . . . . . 78--83 Richard Bagby A Simple Proof that $ \Gamma '(1) = - \gamma $ . . . . . . . . . . . . . . . . 83--85 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 86--93 Jeffrey Nunemacher and Amir Alexander Book Review: \booktitleThe Shape of Content: Creative Writing in Mathematics and Science, by Chandler Davis; Marjorie Wikler Senechal; Jan Zwicky . . . . . . 94--96 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Frank A. Farris The Gini Index and Measures of Inequality . . . . . . . . . . . . . . . 851--864 Gary Gordon and Elizabeth McMahon Moving Faces to Other Places: Facet Derangements . . . . . . . . . . . . . . 865--880 Oleg A. Ivanov On the Number of Regions into Which $n$ Straight Lines Divide the Plane . . . . 881--888 Joel C. Langer and David A. Singer When Is a Curve an Octahedron? . . . . . 889--902 Monique Laurent and Alexander Schrijver On Leonid Gurvits's Proof for Permanents 903--911 Jonathan Sondow and Huang Yi New Wallis- and Catalan-Type Infinite Products for $ \pi $, $e$ and $ \sqrt {2 + \sqrt {2}}$ . . . . . . . . . . . . . 912--917 Nadish de Silva A Concise, Elementary Proof of Arzel\`a's Bounded Convergence Theorem 918--920 Mihály Bessenyei Functional Equations and Finite Groups of Substitutions . . . . . . . . . . . . 921--927 Shibo Liu On the Regularity of Operators Near a Regular Operator . . . . . . . . . . . . 927--928 Gerald A. Edger and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 929--936 Jeffrey Nunemacher and Ethan Akin Book Review: \booktitle[untitled] . . . 937--940 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Natalie Priebe Frank and Sean M. Hart A Dynamical System Using the Voronoï Tessellation . . . . . . . . . . . . . . 99--112 David Sherman Variations on Kuratowski's $ 14$-Set Theorem . . . . . . . . . . . . . . . . 113--123 Tamás Keleti and Elliot Paquette The Trouble with von Koch Curves Built from $n$ gons . . . . . . . . . . . . . 124--137 Lutz Dümbgen and Sara A. van de Geer and Mark C. Veraar and Jon A. Wellner Nemirovski's Inequalities Revisited . . 138--160 John E. Wetzel and Ed Scheinerman An Ancient Elliptic Locus . . . . . . . 161--167 Lara K. Pudwell and Eric S. Rowland Counting Interesting Elections . . . . . 167--174 Sam B. Nadler, Jr. A Proof of Darboux's Theorem . . . . . . 174--175 Emmanuel Lesigne On the Behavior at Infinity of an Integrable Function . . . . . . . . . . 175--181 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 182--189 Jeffrey Nunemacher and Daniel S. Silver Book Review: \booktitle[untitled] . . . 190--192 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Barbara Faires Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2010 to Kenneth A. Ross for Distinguished Service to Mathematics . . 195--197 Marvin Jay Greenberg Old and New Results in the Foundations of Elementary Plane Euclidean and Non-Euclidean Geometries . . . . . . . . 198--219 David A. Levin and Yuval Peres Pólya's Theorem on Random Walks via Pólya's Urn . . . . . . . . . . . . . . . 220--231 Alexander Borisov and Mark Dickinson and Stuart Hastings A Congruence Problem for Polyhedra . . . 232--249 Jan Hilmar and Chris Smyth Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the Euclidean Algorithm . . . . . . . . . . 250--260 Jun Tanaka and Peter F. McLoughlin A Realization of Measurable Sets as Limit Points . . . . . . . . . . . . . . 261--266 Dan McQuillan and R. Bruce Richter A Parity Theorem for Drawings of Complete and Complete Bipartite Graphs 267--273 Sanjay K. Khattri Three Proofs of the Inequality $ e < {\left ({1 + \frac {1}{n}} \right)^{n + 0.5}} $ . . . . . . . . . . . . . . . . 273--277 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 278--285 Anil Nerode Book Review: \booktitle[untitled] . . . 286--288 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Adrian Rice ``To a Factor pr\`es'': Cayley's Partial Anticipation of the Weierstrass $ \wp $-Function . . . . . . . . . . . . . . . 291--302 Geoffrey Pearce Transitive Decompositions of Graphs and Their Links with Geometry and Origami 303--310 Warren P. Johnson Trigonometric Identities \`a la Hermite 311--327 David Burton and John Coleman Quasi-Cauchy Sequences . . . . . . . . . 328--333 Grahame Bennett $p$-Free $ \ell^p$ Inequalities . . . . 334--351 Timothy Marshall A Short Proof of $ \zeta (2) = \pi^2 / 6 $ . . . . . . . . . . . . . . . . . . . 352--353 So Eun Park The Group of Symmetries of the Tower of Hanoi Graph . . . . . . . . . . . . . . 353--360 Li Zhou and Lubomir Markov Recurrent Proofs of the Irrationality of Certain Trigonometric Values . . . . . . 360--362 M. John Curran Groups of Cube-Free Odd Order . . . . . 363--365 Mark Kozek An Asymptotic Formula for Goldbach's Conjecture with Monic Polynomials in $ \mathbb {Z}[x] $ . . . . . . . . . . . . 365--369 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 370--377 Jeffrey Nunemacher and Sanford L. Segal Book Review: \booktitle[untitled] . . . 378--380 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Matthew Richey The Evolution of Markov Chain Monte Carlo Methods . . . . . . . . . . . . . 383--413 A. B. Kharazishvili and T. Sh. Tetunashvili On Some Coverings of the Euclidean Plane with Pairwise Congruent Circles . . . . 414--423 Sherman Stein Transversals in Rectangular Arrays . . . 424--433 Cristinel Mortici Product Approximations via Asymptotic Integration . . . . . . . . . . . . . . 434--441 Francisco J. Freniche On Riemann's Rearrangement Theorem for the Alternating Harmonic Series . . . . 442--448 Richard Steiner Modular Divisor Functions and Quadratic Reciprocity . . . . . . . . . . . . . . 448--451 Peter R. Mercer Another Application of Siebeck's Theorem 452--454 Alan C. Lazer and Mark Leckband The Fundamental Theorem of Algebra via the Fourier Inversion Formula . . . . . 455--457 Gerald A. Edgar and Dough Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 458--465 Jeffrey Nunemacher and Carol S. Schumacher Book Review: \booktitle[untitled] . . . 466--468 Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 469--470 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? James T. Smith Definitions and Nondefinability in Geometry . . . . . . . . . . . . . . . . 475--489 Hartmut Logemann and Eugene P. Ryan Volterra Functional Differential Equations: Existence, Uniqueness, and Continuation of Solutions . . . . . . . 490--511 Stan Gudder Finite Quantum Measure Spaces . . . . . 512--527 David Borwein and Jonathan M. Borwein and Isaac E. Leonard $ L_p $ Norms and the Sinc Function . . 528--539 John H. Elton Indefinite Quadratic Forms and the Invariance of the Interval in Special Relativity . . . . . . . . . . . . . . . 540--547 Brian S. Thomson Monotone Convergence Theorem for the Riemann Integral . . . . . . . . . . . . 547--550 Marco Manetti A Proof of a Version of a Theorem of Hartogs . . . . . . . . . . . . . . . . 550--552 Timothy W. Jones Discovering and Proving that $ \pi $ Is Irrational . . . . . . . . . . . . . . . 553--557 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 558--565 Charles R. Hampton and Jeffrey Nunemacher Book Review: \booktitle[untitled] . . . 566--568 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? William Cavendish and John H. Conway Symmetrically Bordered Surfaces . . . . 571--580 Sam Northshield Stern's Diatomic Sequence $ 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, \ldots {} $ . . . . . 581--598 Peter J. Olver Dispersive Quantization . . . . . . . . 599--610 Thomas Stoll A Fancy Way to Obtain the Binary Digits of $ 759250125 \sqrt {2} $ . . . . . . . 611--617 T. Amdeberhan and O. Espinosa and V. H. Moll and A. Straub Wallis--Ramanujan--Schur--Feynman . . . 618--632 Mike Krebs and Thomas Wright On Cantor's First Uncountability Proof, Pick's Theorem, and the Irrationality of the Golden Ratio . . . . . . . . . . . . 633--637 Filip Najman The Diophantine Equation $ x^4 \pm y^4 = i z^2 $ in Gaussian Integers . . . . . . 637--641 Christopher Frayer and James A. Swenson Polynomial Root Motion . . . . . . . . . 641--646 Aviezri S. Fraenkel From Enmity to Amity . . . . . . . . . . 646--648 Gerald A. Edgar and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 649--656 Jeffrey Nunemacher and Peter Sin Book Review: \booktitle[untitled] . . . 657--660 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Gerald B. Folland A Tale of Topology . . . . . . . . . . . 663--672 Jack S. Calcut Grade School Triangles . . . . . . . . . 673--685 Mark A. Conger and Jason Howald A Better Way to Deal the Cards . . . . . 686--700 Tom M. Apostol and Mamikon A. Mnatsakanian Tanvolutes: Generalized Involutes . . . 701--713 Leonard F. Klosinski and Gerald L. Alexanderson and Loren C. Larson The Seventieth William Lowell Putnam Mathematical Competition . . . . . . . . 714--721 Alin Bostan and Philippe Dumas Wronskians and Linear Independence . . . 722--727 Abbas M. Alhakim A Simple Combinatorial Algorithm for de Bruijn Sequences . . . . . . . . . . . . 728--732 Albert Nijenhuis Short Gamma Products with Simple Values 733--737 Miyeon Kwon Dimension, Linear Functionals, and Norms in a Vector Space . . . . . . . . . . . 738--740 Anonymous Problems and Solutions . . . . . . . . . 741--748 Marion Deutsche Cohen Book Review: \booktitle[untitled] . . . 749--753 Anonymous Back matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ?? Francis Edward Su Teaching Research: Encouraging Discoveries . . . . . . . . . . . . . . 759--769 Harold P. Boas Julius and Julia: Mastering the Art of the Schwarz Lemma . . . . . . . . . . . 770--785 Taras Banakh and Oleg Verbitsky and Yaroslav Vorobets Fermat's Spiral and the Line Between Yin and Yang . . . . . . . . . . . . . . . . 786--800 Karel Hrbacek and Olivier Lessmann and Richard O'Donovan Analysis with Ultrasmall Numbers . . . . 801--816 Hendrik Lenstra Irreducible Cubics Modulo Five . . . . . 817--821 Mateusz Micha\lek A Short Proof of Combinatorial Nullstellensatz . . . . . . . . . . . . 821--823 Sam H. Creswell A Continuous Bijection from $ \ell^2 $ onto a Subset of $ \ell^2 $ Whose Inverse Is Everywhere Discontinuous . . 823--828 Nicolae Anghel On a Question of Connes and Zagier Regarding Parallelograms Inscribed in a Pair of Confocal Ellipses . . . . . . . 828--831 Stephen M. Walk A Streamlined Proof of an Essential Calculus Fact . . . . . . . . . . . . . 832--833 Gerald A. Edger and Doug Hensley and Douglas B. West Problems and Solutions . . . . . . . . . 834--843 Jeffrey Nunemacher and Rebecca F. Goldin Book Review: \booktitle[untitled] . . . 844--847 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 David A. Cox Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First . . . . . . . . . . . . . . . . 3--21 Jennifer M. Johnson and János Kollár How Small Can a Polynomial Be Near Infinity? . . . . . . . . . . . . . . . 22--40 Nikolai V. Ivanov Arnol'd, the Jacobi Identity, and Orthocenters . . . . . . . . . . . . . . 41--65 Nicholas Pippenger Two Extensions of Results of Archimedes 66--71 Paul Pollack On Polynomial Rings with a Goldbach Property . . . . . . . . . . . . . . . . 71--77 Alfonso Villani Measurable Functions with a Given Set of Integrability Exponents . . . . . . . . 77--82 Alexis Akira Toda Operator Reverse Monotonicity of the Inverse . . . . . . . . . . . . . . . . 82--83 Anonymous Problems and Solutions . . . . . . . . . 84--91 Virginia McShane Warfield Book Review: \booktitle[untitled] . . . 92--95 Anonymous Back Matter . . . . . . . . . . . . . . 96--96
Anonymous Front Matter . . . . . . . . . . . . . . 861--862 Henryk Gerlach and Heiko von der Mosel On Sphere-Filling Ropes . . . . . . . . 863--876 Géza Kós On the Grasshopper Problem with Signed Jumps . . . . . . . . . . . . . . . . . 877--886 Giovanni Falcone and Marco Pavone Kirkman's Tetrahedron and the Fifteen Schoolgirl Problem . . . . . . . . . . . 887--900 Paul Baginski and Scott T. Chapman Factorizations of Algebraic Integers, Block Monoids, and Additive Number Theory . . . . . . . . . . . . . . . . . 901--920 Hayri Ardal and Tom Brown and Veselin Jungi\'c Chaotic Orderings of the Rationals and Reals . . . . . . . . . . . . . . . . . 921--925 Raphaël Cerf and Pierre Petit A Short Proof of Cramér's Theorem in $ \mathbb {R} $ . . . . . . . . . . . . . 925--931 Bahman Kalantari A Geometric Modulus Principle for Polynomials . . . . . . . . . . . . . . 931--935 Anonymous Problems and Solutions . . . . . . . . . 936--945 Andrew Odlyzko Book Review: \booktitleExperimental Mathematics in Action, by D. H. Bailey, J. M. Borwein, N. J. Calkin, R. Girgensohn, D. R. Luke, and V. H. Moll. A K Peters, Wellesley, MA, 2007. xii + 322 pp., ISBN 978-1-56881-271-7. \$65} 946--951 Daniel J. Velleman Book Review: \booktitleEndnotes . . . . 952--953 Anonymous Index to Volume 118 . . . . . . . . . . 954--964 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 97--98 David M. Bressoud Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus 99--115 Ravi Vakil The Mathematics of Doodling . . . . . . 116--129 Ian Short Ford Circles, Continued Fractions, and Rational Approximation . . . . . . . . . 130--135 Markus Müller and Dierk Schleicher How to Add a Noninteger Number of Terms: From Axioms to New Identities . . . . . 136--152 Lenny Jones When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers? . . . . . . . . . . . . . . . 153--160 Paul Pollack On Dickson's Theorem Concerning Odd Perfect Numbers . . . . . . . . . . . . 161--164 Eyal Ackerman and Rom Pinchasi and Ludmila Scharf and Marc Scherfenberg Every Simple Arrangement of n Lines Contains an Inducing Simple $n$-gon . . 164--167 José L. Gámez-Merino and Gustavo A. Muñoz-Fernández and Juan B. Seoane-Sepúlveda A Characterization of Continuity Revisited . . . . . . . . . . . . . . . 167--170 Sam Northshield A Short Proof and Generalization of Lagrange's Theorem on Continued Fractions . . . . . . . . . . . . . . . 171--175 Guisong Chang and Chen Xu Generalization and Probabilistic Proof of a Combinatorial Identity . . . . . . 175--177 Anonymous Problems and Solutions . . . . . . . . . 178--185 Jeffrey Nunemacher Book Review: \booktitle[untitled] . . . 186--189 Anonymous Back Matter . . . . . . . . . . . . . . 190--192
Anonymous Front Matter . . . . . . . . . . . . . . 193--194 Barbara Faires Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2011 to Joseph A. Gallian for Distinguished Service to Mathematics . . 195--197 Fernando Q. Gouvêa Was Cantor Surprised? . . . . . . . . . 198--209 Steven H. Weintraub On Legendre's Work on the Law of Quadratic Reciprocity . . . . . . . . . 210--216 Alexander Ryba and Joseph Stern Equimodular Polynomials and the Tritangency Theorems of Euler, Feuerbach, and Guinand . . . . . . . . . 217--228 Keith Burns and Boris Hasselblatt The Sharkovsky Theorem: a Natural Direct Proof . . . . . . . . . . . . . . . . . 229--244 John H. Hubbard and Benjamin E. Lundell A First Look at Differential Algebra . . 245--261 Grant Keady Lines of Best Fit for the Zeros and for the Critical Points of a Polynomial . . 262--264 Sascha Kurz and Rom Pinchasi Regular Matchstick Graphs . . . . . . . 264--267 Edward Chlebus A Recursive Scheme for Improving the Original Rate of Convergence to the Euler--Mascheroni Constant . . . . . . . 268--274 Anonymous Problems and Solutions . . . . . . . . . 275--282 Christopher C. Leary Book Review: \booktitle[untitled] . . . 283--286 Anonymous Back Matter . . . . . . . . . . . . . . 287--288
Anonymous Front Matter . . . . . . . . . . . . . . 289--290 Peter Sarnak Integral Apollonian Packings . . . . . . 291--306 Thomas C. Hull Solving Cubics With Creases: The Work of Beloch and Lill . . . . . . . . . . . . 307--315 Heng Huat Chan and Ling Long and YiFan Yang A Cubic Analogue of the Jacobsthal Identity . . . . . . . . . . . . . . . . 316--326 H. M. Hilden and J. M. Montesinos and D. M. Tejada and M. M. Toro Artifacts for Stamping Symmetric Designs 327--343 Jaume Paradís and Pelegrí Viader and Lluís Bibiloni A New Singular Function . . . . . . . . 344--354 Roger Cooke A Remark on Euclid's Theorem on the Infinitude of the Primes . . . . . . . . 355--358 James Rickards When Is a Polynomial a Composition of Other Polynomials? . . . . . . . . . . . 358--363 Pieter Moree A Top Hat for Moser's Four Mathemagical Rabbits . . . . . . . . . . . . . . . . 364--370 Anonymous Problems and Solutions . . . . . . . . . 371--378 Susan Jane Colley Book Review: \booktitle[untitled] . . . 379--382 Anonymous Back Matter . . . . . . . . . . . . . . 383--384
Anonymous Front Matter . . . . . . . . . . . . . . 385--386 David S. Watkins Francis's Algorithm . . . . . . . . . . 387--403 R. Michael Range Where Are Limits Needed in Calculus? . . 404--417 Vincent Vatter Maximal Independent Sets and Separating Covers . . . . . . . . . . . . . . . . . 418--423 M. Skopenkov Packing a Cake into a Box . . . . . . . 424--433 Alan Tucker What Every Mathematician Should Know about Standards-Based Tests . . . . . . 434--447 Geoffrey R. Robinson Cauchy's Theorem and Sylow's Theorem from the Cyclic Case . . . . . . . . . . 448--449 Alan D. Sokal A Really Simple Elementary Proof of the Uniform Boundedness Theorem . . . . . . 450--452 Marian Deaconescu and Gary L. Walls On the Group of Automorphisms of a Group 452--455 Bogdan Nica The Unreasonable Slightness of $ E_2 $ over Imaginary Quadratic Rings . . . . . 455--462 Anonymous Problems and Solutions . . . . . . . . . 463--470 Peggy Aldrich Kidwell Book Review: \booktitle[untitled] . . . 471--474 Anonymous Back Matter . . . . . . . . . . . . . . 475--476
Anonymous Front Matter . . . . . . . . . . . . . . 477--478 Fred Kuczmarski Roads and Wheels, Roulettes and Pedals 479--496 Martin Griffiths The Golden String, Zeckendorf Representations, and the Sum of a Series 497--507 Rafe Jones Achievement Sets of Sequences . . . . . 508--521 Pamela Gorkin and Elizabeth Skubak Polynomials, Ellipses, and Matrices: Two Questions, One Answer . . . . . . . . . 522--533 Ronald F. Wotzlaw and Günter M. Ziegler A Lost Counterexample and a Problem on Illuminated Polytopes . . . . . . . . . 534--543 János Pach and Ethan Sterling Conway's Conjecture for Monotone Thrackles . . . . . . . . . . . . . . . 544--548 Kieren MacMillan and Jonathan Sondow Proofs of Power Sum and Binomial Coefficient Congruences via Pascal's Identity . . . . . . . . . . . . . . . . 549--551 Caleb Emmons Meromorphic Continuation of Dirichlet Series via Derivations . . . . . . . . . 551--556 Anonymous Problems and Solutions . . . . . . . . . 557--564 Robin Hartshorne Book Review: \booktitle[untitled] . . . 565--568 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 569--570 Kenneth A. Ross Benford's Law, a Growth Industry . . . . 571--583 Graham Everest and Thomas Ward A Repulsion Motif in Diophantine Equations . . . . . . . . . . . . . . . 584--598 Alberto Torchinsky The Fourier Transform and the Wave Equation . . . . . . . . . . . . . . . . 599--609 W. Aitken and F. Lemmermeyer Counterexamples to the Hasse Principle 610--628 Peyman Eslami and Pawel Góra On Eventually Expanding Maps of the Interval . . . . . . . . . . . . . . . . 629--635 Hichem Ben-El-Mechaiekh and Robert W. Dimand A Simpler Proof of the von Neumann Minimax Theorem . . . . . . . . . . . . 636--641 Luigi Pace Probabilistically Proving that $ \zeta (2) = \pi^2 / 6 $ . . . . . . . . . . . 641--643 M. Ram Murty and V. Kumar Murty On a Problem of Ruderman . . . . . . . . 644--650 Alan F. Beardon Cyclic Absolute Differences of Integers 650--652 Anonymous Problems and Solutions . . . . . . . . . 653--660 Peter Winkler Book Review: \booktitle[untitled] . . . 661--664 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 665--666 Murad \HOzaydìn and Charlotte Simmons The Birthday Trick with Lies . . . . . . 667--679 Russell A. Gordon Semiperimeter and Pythagorean Triples 680--692 A. B. Kharazishvili Measurability Properties of Vitali Sets 693--703 Stephan Ramon Garcia and Vincent Selhorst-Jones and Daniel E. Poore and Noah Simon Quotient Sets and Diophantine Equations 704--711 P. J. Giblin and J. P. Warder Reconstruction from Medial Representations . . . . . . . . . . . . 712--725 Leonard F. Klosinski and Gerald L. Alexanderson and Loren C. Larson and Mark Krusemeyer The Seventy-First William Lowell Putnam Mathematical Competition . . . . . . . . 726--733 R. K. Oliver On the Parity of a Permutation . . . . . 734--735 Wouter Kager The Hitting Time Theorem Revisited . . . 735--737 R. Thangadurai and A. Vatwani The Least Prime Congruent to One Modulo $n$ . . . . . . . . . . . . . . . . . . 737--742 Penghao Cao and Liping Yuan A Blichfeldt-type Theorem for $H$-points 743--746 Anonymous Problems and Solutions . . . . . . . . . 747--754 Richard Askey Book Review: \booktitle[untitled] . . . 755--762 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 765--766 Bruce C. Berndt The Chief Accountant and Mathematical Friend of Ramanujan --- S. Narayana Aiyar . . . . . . . . . . . . . . . . . 767--776 P. Haxell On Forming Committees . . . . . . . . . 777--788 Tom M. Apostol and Mamikon A. Mnatsakanian Complete Dissections: Converting Regions and Their Boundaries . . . . . . . . . . 789--798 Giacomo Drago and Pier Domenico Lamberti and Paolo Toni A ``Bouquet'' of Discontinuous Functions for Beginners in Mathematical Analysis 799--811 John B. Cosgrave and Karl Dilcher An Introduction to Gauss Factorials . . 812--829 S. P. Glasby Enumerating the Rationals from Left to Right . . . . . . . . . . . . . . . . . 830--835 Semyon N. Litvinov On the Banach--Steinhaus Theorem for Topological Groups . . . . . . . . . . . 836--838 Michael D. Hirschhorn Ramanujan's ``Most Beautiful Identity'' 839--845 Anonymous Problems and Solutions . . . . . . . . . 846--853 Matthew Richey Book Review: \booktitle[untitled] . . . 854--858 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Scott Chapman A Letter from the Editor . . . . . . . . 3--3 Daniel Brinkman and Peter J. Olver Invariant Histograms . . . . . . . . . . 4--24 Thomas Bauer and Mirel Caib\uar and Gary Kennedy Zariski Decomposition: a New (Old) Chapter of Linear Algebra . . . . . . . 25--41 Dan Kalman and Mark McKinzie Another Way to Sum a Series: Generating Functions, Euler, and the Dilog Function 42--51 Costas J. Efthimiou A Class of Periodic Continued Radicals 52--58 Parames Laosinchai and Bhinyo Panijpan A Geometric Interpretation of Pascal's Formula for Sums of Powers of Integers 58--64 Pete L. Clark Covering Numbers in Linear Algebra . . . 65--67 Anonymous Problems and Solutions . . . . . . . . . 68--75 Alan Durfee Book Review: \booktitle[untitled] . . . 76--82 Anonymous Back Matter . . . . . . . . . . . . . . 83--84
Anonymous Front Matter . . . . . . . . . . . . . . 85--86 Boris S. Mordukhovich and Nguyen Mau Nam and Juan Salinas, Jr. Solving a Generalized Heron Problem by Means of Convex Analysis . . . . . . . . 87--99 Sam Vandervelde Jacobi Sum Matrices . . . . . . . . . . 100--114 Donald J. Bindner and Martin Erickson Alcuin's Sequence . . . . . . . . . . . 115--121 Burkard Polster and Marty Ross and David Treeby A Case of Continuous Hangover . . . . . 122--139 David A. Herron Riemann Maps and Diameter Distance . . . 140--147 Cristinel Mortici A Power Series Approach to Some Inequalities . . . . . . . . . . . . . . 147--151 Julian Rosen and Zachary Scherr and Benjamin Weiss and Michael E. Zieve Chebyshev Mappings of Finite Fields . . 151--155 Igor Pak and Rom Pinchasi Collapsing Walls Theorem . . . . . . . . 156--160 Anonymous Problems and Solutions . . . . . . . . . 161--168 José Ferreirós Book Review: \booktitle[untitled] . . . 169--176 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 177--178 Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2012 to John Ewing for Distinguished Service to Mathematics . . 179--182 Jessica Sidman An Introduction to Algebraic Geometry: Polygons, Parameterizations, and Equations . . . . . . . . . . . . . . . 183--198 Daniel Daners The Mercator and Stereographic Projections, and Many in Between . . . . 199--210 Yves Nievergelt Real and Generic Data without Unconstrained Best-Fitting Verhulst Curves and Sufficient Conditions for Median Mitscherlich and Verhulst Curves to Exist . . . . . . . . . . . . . . . . 211--234 William C. Waterhouse Square Root as a Homomorphism . . . . . 235--239 Michael P. Cohen Sample Means of Independent Standard Cauchy Random Variables Are Standard Cauchy: a New Approach . . . . . . . . . 240--244 Daniel Reem Character Analysis Using Fourier Series 245--246 Anonymous Problems and Solutions . . . . . . . . . 247--254 Gerald L. Alexanderson Book Review: \booktitleLoving and Hating Mathematics: Challenging the Myths of Mathematical Life, by Reuben Hersh and Vera John-Steiner. Princeton University Press, Princeton, NJ, 2011, xii + 416 pp. ISBN 978-0-691-14247-0, \$29.95} . . 255--259 Anonymous Back Matter . . . . . . . . . . . . . . 260--260
Anonymous Front Matter . . . . . . . . . . . . . . 261--262 Rachel Wells Hall and Dmitri Tymoczko Submajorization and the Geometry of Unordered Collections . . . . . . . . . 263--283 Stephen McAdam Unknowable Matters: How Nature's Speed Limit on Communication Relates to Quantum Physics . . . . . . . . . . . . 284--299 Barry Cox and Stan Wagon Drilling for Polygons . . . . . . . . . 300--312 Kenneth Hicks and Xiang-dong Hou and Gary L. Mullen Sums of Reciprocals of Polynomials over Finite Fields . . . . . . . . . . . . . 313--317 Evgeny Lakshtanov and Vera Roshchina On Finiteness in the Card Game of War 318--323 Djurdje Cvijovi\'c and Hari M. Srivastava Limit Representations of Riemann's Zeta Function . . . . . . . . . . . . . . . . 324--330 Christian Elsholtz Prime Divisors of Thin Sequences . . . . 331--333 I. E. Leonard and A. C. F. Liu A Familiar Recurrence Occurs Again . . . 333--336 Robbert Fokkink Tossing Coins to Guess a Secret Number 337--339 Lizhou Chen A Generalization of the Cayley--Hamilton Theorem . . . . . . . . . . . . . . . . 340--342 R. McCutcheon Monochromatic Permutation Quadruples --- a Schur Thing in $ S_n $ . . . . . . . . 342--343 Anonymous Problems and Solutions . . . . . . . . . 344--351 Bonnie Shulman Book Review: \booktitlePopulation Games and Evolutionary Dynamics, by William H. Sandholm. MIT Press, Cambridge, MA, 2011, xxv + 589 pp., ISBN 978-0-262-19587-4, \$65} . . . . . . . . 352--356 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 357--358 Tony Gilbert Lost Mail: The Missing Envelope in the Problem of the Minimal Surface of Revolution . . . . . . . . . . . . . . . 359--372 Frits Beukers and Florian Luca and Frans Oort Power Values of Divisor Sums . . . . . . 373--380 Hassan Boualem and Robert Brouzet On What Is the Almost-Near Principle . . 381--397 Serge Tabachnikov The (Un)equal Tangents Problem . . . . . 398--405 Lance Bryant and James Hamblin and Lenny Jones A Variation on the Money-Changing Problem . . . . . . . . . . . . . . . . 406--414 David Callan Flexagons Lead to a Catalan Number Identity . . . . . . . . . . . . . . . . 415--419 R. D. Arthan Aronszajn's Criterion for Euclidean Space . . . . . . . . . . . . . . . . . 419--422 Joseph E. Borzellino and Morgan Sherman When Is a Trigonometric Polynomial Not a Trigonometric Polynomial? . . . . . . . 422--425 Anonymous Problems and Solutions . . . . . . . . . 426--433 James A. Walsh Book Review: \booktitleRandomness and Recurrence in Dynamical Systems, by Rodney Nillsen. The Carus Mathematical Monographs Number 31, Mathematical Association of America, Washington, DC, 2010, xviii + 357 pp., ISBN 978-0-88385-043-5, \$52.95} . . . . . . 434--438 Anonymous Back Matter . . . . . . . . . . . . . . 439--440
Anonymous Front Matter . . . . . . . . . . . . . . 441--442 Dimitris Koukoulopoulos and Johann Thiel Arrangements of Stars on the American Flag . . . . . . . . . . . . . . . . . . 443--450 Fred Kuczmarski Rolling Sinusoidal Spirals . . . . . . . 451--467 Robert Mandl and Thomas Pühringer and Maximilian Thaler Analytic Approach to Galileo's Theorem on the Descent Time Along Two-Chord Paths in a Circle . . . . . . . . . . . 468--476 Paul Binding and Hans Volkmer A Prüfer Angle Approach to the Periodic Sturm--Liouville Problem . . . . . . . . 477--484 Raymond Mortini and Rudolf Rupp Mappings into the Euclidean Sphere . . . 485--494 Branko Grünbaum Is Napoleon's Theorem Really Napoleon's Theorem? . . . . . . . . . . . . . . . . 495--501 Michael J. Dorfling and Johan H. Meyer On Polynomials and Divisibility . . . . 502--506 Pedro Roitman Gaussian Curvature, Mirrors, and Maps 506--509 Alan J. Aw The Turán Number and Probabilistic Combinatorics . . . . . . . . . . . . . 510--513 Walter Wyss Perfect Parallelograms . . . . . . . . . 513--515 Timothy C. Wallstrom The Equalization Probability of the Pólya Urn . . . . . . . . . . . . . . . . . . 516--518 Lars Holst A Proof of Euler's Infinite Product for the Sine . . . . . . . . . . . . . . . . 518--521 Anonymous Problems and Solutions . . . . . . . . . 522--529 Jennifer J. Quinn Book Review: \booktitleCombinatorics the Rota Way, by Joseph P. S. Kung, Gian-Carlo Rota, and Catherine H. Yan. Cambridge University Press, New York, 2009, xii + 396 pp., ISBN 978-0-521-73794-4, \$40.99} . . . . . . 530--532 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 533--534 David Borwein and Jonathan M. Borwein and Armin Straub A Sinc that Sank . . . . . . . . . . . . 535--549 Lionel Levine and Katherine E. Stange How to Make the Most of a Shared Meal: Plan the Last Bite First . . . . . . . . 550--565 Kai F. Kristensen A Nearest Integer Solution to the Longest Run of Randomly Generated Words 566--572 F. Lemmermeyer Parametrization of Algebraic Curves from a Number Theorist's Point of View . . . 573--583 Peter Borwein and Joe Hobart The Extraordinary Power of Division in Straight Line Programs . . . . . . . . . 584--592 Alin Bostan and Thierry Combot A Binomial-like Matrix Equation . . . . 593--597 Ezra Brown and Marc Chamberland Generalizing Gauss's Gem . . . . . . . . 597--601 Greg Kuperberg Norms as a Function of p Are Linearly Independent in Finite Dimensions . . . . 601--603 Cédric De Groote and Mitia Duerinckx Functions with Constant Mean on Similar Countable Subsets of $ \mathbb {R}^2 $ 603--605 Tomasz Tkocz An Upper Bound for Spherical Caps . . . 606--607 Anonymous Problems and Solutions . . . . . . . . . 608--615 Marion Cohen Book Review: \booktitleChange Is Possible: Stories of Women and Minorities in Mathematics, by Patricia Clark Kenschaft. American Mathematical Society, Providence, RI, 2005, ix + 211 pp., ISBN 0-8218-3748-6, \$32.00} . . . 616--620 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 621--622 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Second William Lowell Putnam Mathematical Competition . . . . . . . . 623--635 Yuval Ginosar and Ilan Yona A Model for Pairs of Beatty Sequences 636--645 David H. Bailey and Jonathan M. Borwein Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics . . . . . 646--657 Bruce Ebanks Looking for a Few Good Means . . . . . . 658--669 Paul Pollack Finiteness Theorems for Perfect Numbers and Their Kin . . . . . . . . . . . . . 670--681 Akira Sakurai Vector Analysis Proof of Erd\Hos' Inequality for Triangles . . . . . . . . 682--684 Boris M. Makarov Calculation of the Volume of Multidimensional Cones and Balls Using Cavalieri's Principle . . . . . . . . . 685--689 David Angell Evaluation of Certain Legendre Symbols 690--693 Jonathan Groves An Elementary Counterexample in the Compact-Open Topology . . . . . . . . . 693--694 Robert Dawson Arithmetic Polygons . . . . . . . . . . 695--698 Anonymous Problems and Solutions . . . . . . . . . 699--706 Mark Schwartz Book Review: \booktitleGeometry for College Students, by I. Martin Isaacs. American Mathematical Society, The Sally Series, Pure and Applied Undergraduate Texts No. 8, Providence, RI, 2001. vii + 222 pp., ISBN 978-0-8218-4794-7. \$62 (\$49.60 to AMS members) . . . . . . . . 707--711 Anonymous Back Matter . . . . . . . . . . . . . . 712--712
Anonymous Front Matter . . . . . . . . . . . . . . 713--714 Michael Eisermann The Fundamental Theorem of Algebra Made Effective: An Elementary Real-Algebraic Proof via Sturm Chains . . . . . . . . . 715--752 Oswaldo Rio Branco de Oliveira The Fundamental Theorem of Algebra: From the Four Basic Operations . . . . . . . 753--758 John Lorch Magic Squares and Sudoku . . . . . . . . 759--770 Panagiota N. Panagopoulou and Paul G. Spirakis Playing a Game to Bound the Chromatic Number . . . . . . . . . . . . . . . . . 771--778 David Brink The Spiral of Theodorus and Sums of Zeta-values at the Half-integers . . . . 779--786 B. Shapiro and M. Shapiro A Few Riddles Behind Rolle's Theorem . . 787--793 Boris Alexeev and Jacob Tsimerman Note on a War-like Card Game . . . . . . 793--795 Florian Breuer Newton Identities for Weierstrass Products . . . . . . . . . . . . . . . . 796--799 Anonymous Problems and Solutions . . . . . . . . . 800--807 Stan Wagon Book Review: \booktitleIn Pursuit of the Traveling Salesman, by William J. Cook. Princeton University Press, Princeton, NJ, 2012 xiii + 228 pp., ISBN 978-0-691-15270-7, \$27.95} . . . . . . 808--811 Anonymous Back Matter . . . . . . . . . . . . . . 812--812
Anonymous Front Matter . . . . . . . . . . . . . . 813--814 Tanya Khovanova and Alexey Radul Killer Problems . . . . . . . . . . . . 815--823 Robert T. Jantzen and Klaus Volpert On the Mathematics of Income Inequality: Splitting the Gini Index in Two . . . . 824--837 Carla D. Martin and Mason A. Porter The Extraordinary SVD . . . . . . . . . 838--851 William F. Trench An Elementary View of Weyl's Theory of Equal Distribution . . . . . . . . . . . 852--861 Yong-Gao Chen and Min Tang On the Elementary Symmetric Functions of $1$, $ 1 / 2$, \ldots, $ 1 / n$ . . . . 862--867 Rolfdieter Frank and Harald Riede Hyperplane Sections of the $n$-Dimensional Cube . . . . . . . . . . 868--872 Jacob A. Siehler Tiling Hamiltonian Cycles on the $ 24$-Cell . . . . . . . . . . . . . . . . 872--875 Witold Sadowski A Toy Forecast Model . . . . . . . . . . 876--879 Anonymous Problems and Solutions . . . . . . . . . 880--887 Gerald L. Alexanderson Book Review: \booktitleTranscending Tradition: Jewish Mathematicians in German-Speaking Academic Culture, by Birgit Bergmann, Moritz Epple, and Ruti Ungar, editors. Springer Verlag, Berlin and Heidelberg, 2012, xi + 289 pp., ISBN 978-3-642-22463-8, \$49.95} . . . . . . 888--891 Anonymous Editor's Endnotes . . . . . . . . . . . 892--894 Anonymous Title Index, Author Index, Problems Proposed, Problems Solved, Solutions, Referees . . . . . . . . . . . . . . . . 895--905 Anonymous Back Matter . . . . . . . . . . . . . . 906--908
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Nicholas R. Baeth and Roger Wiegand Factorization Theory and Decompositions of Modules . . . . . . . . . . . . . . . 3--34 Steven J. Brams and Michael A. Jones and Christian Klamler $N$-Person Cake-Cutting: There May Be No Perfect Division . . . . . . . . . . . . 35--47 M. Ram Murty and Anastasia Zaytseva Transcendence of Generalized Euler Constants . . . . . . . . . . . . . . . 48--54 Jean-Baptiste Hiriart-Urruty and Patrice Lass\`ere When Is $ L^r(R) $ Contained in $ L^p(R) + L^q(R) $? . . . . . . . . . . . . . . 55--61 Vinicius Nicolae Petre Anghel A Use of Symmetry: Generalization of an Integral Identity Found by M. L. Glasser 62--69 Yi Jun Chen A Proof that Zeilberger Missed: a New Proof of an Identity by Chaundy and Bullard Based on the Wilf--Zeilberger Method . . . . . . . . . . . . . . . . . 69--70 L. P. Withers, Jr. Visual Angular Momentum: Mamikon Meets Kepler . . . . . . . . . . . . . . . . . 71--73 Wlodzimierz Bak A Simple Characterization of Differentiation . . . . . . . . . . . . 74--75 Anonymous Problems and Solutions . . . . . . . . . 76--83 Fernando Q. Gouvêa Book Review: \booktitleElliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library IAS/Park City Subseries, vol, by Álvaro Lozano-Robledo. 58), American Mathematical Society, Providence, RI, 2011, 195 pp., ISBN 978-0-8218-5242-2, \$29.60} . . . . . . . . . . . . . . . . 84--94 Anonymous Back Matter . . . . . . . . . . . . . . 95--96
Anonymous Front Matter . . . . . . . . . . . . . . 97--98 Holger Teismann Toward a More Complete List of Completeness Axioms . . . . . . . . . . 99--114 Freeman J. Dyson and Norman E. Frankel and M. Lawrence Glasser Lehmer's Interesting Series . . . . . . 116--130 Dexter Kozen and Alexandra Silva On Moessner's Theorem . . . . . . . . . 131--139 Susan H. Marshall and Alexander R. Perlis Heronian Tetrahedra Are Lattice Tetrahedra . . . . . . . . . . . . . . . 140--149 Jeremy Alm and Michael Gramelspacher and Theodore Rice Rubik's on the Torus . . . . . . . . . . 150--160 David C. Ullrich A Simple Elementary Proof of Hilbert's Inequality . . . . . . . . . . . . . . . 161--164 Aaron Melman The Twin of a Theorem by Cauchy . . . . 164--168 Marco Dalai How Would Riemann Evaluate $ \zeta (2 n) $? . . . . . . . . . . . . . . . . . . . 169--171 Vladimir Dragovi\'c Polynomial Dynamics and a Proof of the Fermat Little Theorem . . . . . . . . . 171--173 Anonymous Problems and Solutions . . . . . . . . . 174--181 Michael Nathanson Book Review: \booktitleElements of Information Theory, by Thomas M. Cover and Joy A. Thomas. John Wiley and Sons, Inc., Hoboken, NJ, 2006, xxiv + 748 pp., ISBN 0-471-24195-4, \$111.00} . . . . . 182--187 Anonymous Back Matter . . . . . . . . . . . . . . 188--188
Anonymous Front Matter . . . . . . . . . . . . . . 189--190 Dierk Schleicher and Serge Tabachnikov Letter from the Guest Editors . . . . . 191--191 John H. Conway On Unsettleable Arithmetical Problems 192--198 Robert Foote and Mark Levi and Serge Tabachnikov Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture . . . . . . . . . . . . . . . 199--216 Dmitry Fuchs Evolutes and Involutes of Spatial Curves 217--231 Étienne Ghys Intersecting Curves (Variation on an Observation of Maxim Kontsevich) . . . . 232--242 Aimeric Malter and Dierk Schleicher and Don Zagier New Looks at Old Number Theory . . . . . 243--264 Tadashi Tokieda Roll Models . . . . . . . . . . . . . . 265--282 Rade T. Zivaljevi\'c Book Review: \booktitleMathematical Omnibus: Thirty Lectures on Classic Mathematics, by Dmitry Fuchs and Serge Tabachnikov. American Mathematical Society, Providence, RI, 2007, xv + 463 pp., ISBN-13: 978-0-8218-4316-1, \$61} 283--286 Pieter Moree Book Review: \booktitleAn Invitation to Mathematics: From Competitions to Research, [edited] by Dierk Schleicher and Malte Lackmann, editors. Springer-Verlag, Heidelberg, 2011, xiv + 220 pp. ISBN-13: 978-3-642-19532-7, \$34.95} . . . . . . . . . . . . . . . . 286--288 Christoph Pöppe Book Review: \booktitleDimensions, by Jos Leys, Étienne Ghys, and Aurélien Alvarez. A mathematical video. \urlwww.dimensions-math.org, 117 minutes, no cost . . . . . . . . . . . . 288--290 Anonymous Back Matter . . . . . . . . . . . . . . 291--292
Anonymous Front Matter . . . . . . . . . . . . . . 293--294 Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2013 to William A. Hawkins for Distinguished Service to Mathematics . . 295--297 Tom M. Apostol and Mamikon A. Mnatsakanian New Balancing Principles Applied to Circumsolids of Revolution, and to $n$-Dimensional Spheres, Cylindroids, and Cylindrical Wedges . . . . . . . . . 298--321 Matthew Jenssen and Daniel Montealegre and Vadim Ponomarenko Irreducible Factorization Lengths and the Elasticity Problem within $ \mathbb {N} $ . . . . . . . . . . . . . . . . . 322--328 Kenneth S. Williams The Parents of Jacobi's Four Squares Theorem Are Unique . . . . . . . . . . . 329--345 Kathryn L. Nyman and Francis Edward Su A Borsuk--Ulam Equivalent that Directly Implies Sperner's Lemma . . . . . . . . 346--354 Habib Bin Muzaffar A New Proof of a Classical Formula . . . 355--358 Steve Alpern and Robbert Fokkink Illuminating a Network from Its Nodes 358--359 Orr Moshe Shalit A Sneaky Proof of the Maximum Modulus Principle . . . . . . . . . . . . . . . 359--362 Olivier Bernardi A Short Proof of Rayleigh's Theorem with Extensions . . . . . . . . . . . . . . . 362--364 Anonymous Problems and Solutions . . . . . . . . . 365--372 Marie Snipes Book Review: \booktitleLinear and Nonlinear Programming, 3rd ed, by David G. Luenberger and Yinyu Ye., Springer, New York, 2008, xiv + 546 pp., ISBN 0-387-74502-5, \$109} . . . . . . . . . 373--379 Anonymous Back Matter . . . . . . . . . . . . . . 380--380
Anonymous Front Matter . . . . . . . . . . . . . . 381--382 Scott Chapman A Letter from the Editor . . . . . . . . 383--383 Ehud Kalai Foreword: The High Priest of Game Theory 384--385 D. Gale and L. S. Shapley College Admissions and the Stability of Marriage . . . . . . . . . . . . . . . . 386--391 James Propp Real Analysis in Reverse . . . . . . . . 392--408 Melvyn B. Nathanson On the Fractional Parts of Roots of Positive Real Numbers . . . . . . . . . 409--429 Stephen M. Buckley and Desmond MacHale Variations on a Theme: Rings Satisfying $ x^3 = x $ Are Commutative . . . . . . 430--440 Joshua Cooper and Aaron Dutle Greedy Galois Games . . . . . . . . . . 441--451 Rachid Marsli and Frank J. Hall Geometric Multiplicities and Gersgorin Discs . . . . . . . . . . . . . . . . . 452--455 Jim X. Xiang A Note on the Cauchy--Schwarz Inequality 456--459 Costas J. Efthimiou A Class of Continued Radicals . . . . . 459--461 D. Aharonov and U. Elias A Binomial Identity via Differential Equations . . . . . . . . . . . . . . . 462--466 F. Galaz-Fontes Another Proof for Non-Supercyclicity in Finite Dimensional Complex Banach Spaces 466--468 Anonymous Problems and Solutions . . . . . . . . . 469--476 Kevin Woods Book Review: \booktitleSymmetry: A Mathematical Exploration, by Kristopher Tapp. Springer, New York, 2012, xiv + 215pp., ISBN 978-1-4614-0298-5, \$49.95} 477--481 Anonymous Editor's Endnotes . . . . . . . . . . . 482--483 Anonymous Back Matter . . . . . . . . . . . . . . 484--484
Anonymous Front Matter . . . . . . . . . . . . . . 485--486 Andrew D. Hwang Paper Surface Geometry . . . . . . . . . 487--499 Joanna M. Papakonstantinou and Richard A. Tapia Origin and Evolution of the Secant Method in One Dimension . . . . . . . . 500--518 Nathan Bliss and Ben Fulan and Stephen Lovett and Jeff Sommars Strong Divisibility, Cyclotomic Polynomials, and Iterated Polynomials 519--536 Steven H. Weintraub Several Proofs of the Irreducibility of the Cyclotomic Polynomials . . . . . . . 537--545 Kurt Girstmair The Equation $ x^2 + \bar {m} y^2 = \bar {k} $ in $ \mathbb {Z} / p \mathbb {Z} $ 546--552 Claire-Soizic Henry Coxeter Friezes and Triangulations of Polygons . . . . . . . . . . . . . . . . 553--558 Jonathon Peterson A Probabilistic Proof of a Binomial Identity . . . . . . . . . . . . . . . . 558--562 S. A. Rankin The Euclidean Algorithm and the Linear Diophantine Equation $ a x + b y = {\rm gcd}(a, b) $ . . . . . . . . . . . . . . 562--564 Tadashi Tokieda A Buoyancy-Driven Perpetual Motion Machine . . . . . . . . . . . . . . . . 564--566 Manas R. Sahoo Example of a Monotonic, Everywhere Differentiable Function on $ \mathbb {R} $ Whose Derivative Is not Continuous . . 566--568 Anonymous Problems and Solutions . . . . . . . . . 569--576 David Bressoud Book Review: \booktitleCalculus, by Michael Spivak; \booktitleCalculus Deconstructed: A Second Course in First-Year Calculus. MAA Textbooks, Mathematical Association of America, Washington, DC, 2009, xvi + 491 pp., ISBN 978-0-88385-756-4, \$ 59.95. by Zbigniew Nitecki; \booktitle{Approximately Calculus}. American Mathematical Society, Providence, RI, 2006, xvii + 292 pp., ISBN 978-0-8218-3750-4, \$50.00. by Shahriar Sharhriari; \booktitleGuide to Cauchy's Calculus: A Translation and Analysis of Calcul Infinitésimal. Fairview Academic Press, Walnut Creek, CA, 2012, viii + 616 pp., ISBN 978-0-9838837-0-8, \$139.00. by Dennis M. Cates; \booktitle{The Calculus Integral}. ClassicalRealAnalysis.com, Charleston, SC, 2010, x + 291, ISBN 978-1442180956, \$14.95. by Brian S. Thomson. 4th edition. Publish or Perish, Houston, TX, 2008, xiv + 680 pp., ISBN 978-0-914098-91-1, \$85.00} . . . . . . 577--580 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 581--582 David J. Aldous Using Prediction Market Data to Illustrate Undergraduate Probability . . 583--593 Stephen D. Casey and Brian M. Sadler Pi, the Primes, Periodicities, and Probability . . . . . . . . . . . . . . 594--608 Peter Kuchment and Sergey Lvin Identities for $ \sin x $ that Came from Medical Imaging . . . . . . . . . . . . 609--621 Steve Butler and Ron Graham Subdivision Using Angle Bisectors Is Dense in the Space of Triangles . . . . 622--630 Mikhail G. Katz and Eric Leichtnam Commuting and Noncommuting Infinitesimals . . . . . . . . . . . . . 631--641 Daniele Ritelli Another Proof of $ {\zeta (2) = \frac {\pi^2}{6}} $ Using Double Integrals . . 642--645 Matthias Arnold and Werner Glaß Simple Approximation Formulas for the Birthday Problem . . . . . . . . . . . . 645--648 Anthony J. Bevelacqua Another Irreducibility Criterion . . . . 648--650 Jaban Meher and M. Ram Murty Ramanujan's Proof of Bertrand's Postulate . . . . . . . . . . . . . . . 650--653 T. Samuel A Simple Proof of Vitali's Theorem for Signed Measures . . . . . . . . . . . . 654--659 Anonymous Problems and Solutions . . . . . . . . . 660--669 Joseph Malkevitch Book Review: \booktitleThe Mathematical Coloring Book, by Alexander Soifer. Springer, New York, xxx + 607 pp., ISBN 978-0-387-74640-1, \$69.95} . . . . . . 670--674 Samuel G. Moreno and Esther M. García-Caballero Book Review: \booktitleOn the Irrationality of $ \surd 2 $ Once Again 674--674 Anonymous Back Matter . . . . . . . . . . . . . . 675--676
Anonymous Front Matter . . . . . . . . . . . . . . 677--678 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Third William Lowell Putnam Mathematical Competition . . . . . . . . 679--688 Alan Tucker The History of the Undergraduate Program in Mathematics in the United States . . 689--705 Brant Jones and Laura Taalman and Anthony Tongen Solitaire Mancala Games and the Chinese Remainder Theorem . . . . . . . . . . . 706--724 Paul Monsky Frobenius' Result on Simple Groups of Order $ \frac {p^3 - p^2}{2} $ . . . . . 725--732 Bhaskar Bagchi and Basudeb Datta Higher-Dimensional Analogues of the Map Coloring Problem . . . . . . . . . . . . 733--737 Dorin Ervin Dutkay and Constantin P. Niculescu and Florin Popovici Stirling's Formula and Its Extension for the Gamma Function . . . . . . . . . . . 737--740 Jean Van Schaftingen A Direct Proof of the Existence of Eigenvalues and Eigenvectors by Weierstrass's Theorem . . . . . . . . . 741--746 A. G. Ramm A Variational Principle and Its Application to Estimating the Electrical Capacitance of a Perfect Conductor . . . 747--751 Zsolt Lengvárszky Proving the Pythagorean Theorem via Infinite Dissections . . . . . . . . . . 751--753 Anonymous Problems and Solutions . . . . . . . . . 754--761 Takis Konstantopoulos Book Review: \booktitleAn Introduction to Measure Theory, by Terence Tao. American Mathematical Society, Providence RI, 2011, xvi + 206 pp., ISBN 978-0-8218-6919-2, \$53.00} . . . . . . 762--768 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 769--770 Jacques Lévy Véhel and Franklin Mendivil Christiane's Hair . . . . . . . . . . . 771--786 Daniel J. Velleman and Gregory S. Warrington What to Expect in a Game of Memory . . . 787--805 Antonín Slavík Mixing Problems with Many Tanks . . . . 806--821 Jonathan Bayless and Dominic Klyve Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers 822--831 Jorge Luis Cimadevilla Villacorta Certain Inequalities Associated with the Divisor Function . . . . . . . . . . . . 832--837 Charles S. Kahane On the Nonexistence of Certain Limits for the Complex Exponential . . . . . . 837--840 Árpád Bényi and Branko \'Curgus A Generalization of Routh's Triangle Theorem . . . . . . . . . . . . . . . . 841--846 David Pan A Maximum Principle for High-Order Derivatives . . . . . . . . . . . . . . 846--848 Gerhard J. Woeginger Nothing New about Equiangular Polygons 849--850 Stephan Ramon Garcia Quotients of Gaussian Primes . . . . . . 851--853 Anonymous Problems and Solutions . . . . . . . . . 854--861 Betty Mayfield Book Review: \booktitleCalculus: Modeling and Application, second edition, by David A. Smith and Lawrence C. Moore. Mathematical Association of America, Washington, D.C., 2010. http://maa.pinnaclecart.com. Price: \$35.00. ISBN 978-1-6144-610-1} . . . . 862--864 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 865--866 David Pengelley Quick, Does $ 23 / 67 $ Equal $ 33 / 97 $ ? A Mathematician's Secret from Euclid to Today . . . . . . . . . . . . . . . . 867--876 Alexander P. Campbell and Daniel Daners Linear Algebra via Complex Analysis . . 877--892 Olle Häggström and Johan Wästlund Rigorous Computer Analysis of the Chow--Robbins Game . . . . . . . . . . . 893--900 Will Traves From Pascal's Theorem to $d$-Constructible Curves . . . . . . . . 901--915 Roger E. Howe The Cuoco Configuration . . . . . . . . 916--923 Ulrich Abel A Generalization of the Leibniz Rule . . 924--928 Jonathan Sondow The Parbelos, a Parabolic Analog of the Arbelos . . . . . . . . . . . . . . . . 929--935 G. J. O. Jameson Inequalities for Gamma Function Ratios 936--940 Anonymous Problems and Solutions . . . . . . . . . 941--948 James M. Henle and Michael G. Henle Book Review: \booktitleReal Analysis Through Modern Infinitesimals, Cambridge University Press, 2011, xix + 565 pp, by Nader Vakil., ISBN 978-1-107-00202-9, \$127.00} . . . . . . . . . . . . . . . 949--953 Anonymous Editor's Endnotes . . . . . . . . . . . 954--956 Anonymous Title Index, Author Index, Problems Proposed, Problems Solved, Solutions, Referees . . . . . . . . . . . . . . . . 957--967 Anonymous Back Matter . . . . . . . . . . . . . . 968--968
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Scott T. Chapman A Letter from the Editor: What's In a Color? . . . . . . . . . . . . . . . . . 3--4 Melvyn B. Nathanson Additive Systems and a Theorem of de Bruijn . . . . . . . . . . . . . . . . . 5--17 Mario Ponce and Patricio Santibáñez On Equidistant Sets and Generalized Conics: The Old and the New . . . . . . 18--32 Anthony Mendes and Kent E. Morrison Guessing Games . . . . . . . . . . . . . 33--44 Chris D. Lynd Using Difference Equations to Generalize Results for Periodic Nested Radicals . . 45--59 J. A. Conejero and P. Jiménez-Rodríguez and G. A. Muñoz-Fernández and J. B. Seoane-Sepúlveda When the Identity Theorem ``Seems'' to Fail . . . . . . . . . . . . . . . . . . 60--68 Ádám Besenyei Peano's Unnoticed Proof of Borel's Theorem . . . . . . . . . . . . . . . . 69--72 Steven H. Weintraub Values of Polynomials over Integral Domains . . . . . . . . . . . . . . . . 73--74 Bao Qin Li A Direct Proof and a Transcendental Version of the Fundamental Theorem of Algebra via Cauchy's Theorem . . . . . . 75--77 Samuel Clowes Huneke An Inductive Proof of Hex Uniqueness . . 78--80 Karim Boulabiar Real-Valued Ring Homomorphisms on $ C(\Omega) $ . . . . . . . . . . . . . . 81--82 Anonymous Problems and Solutions . . . . . . . . . 83--90 Kenneth A. Ross Book Review: \booktitleIn the Dark on the Sunny Side: a Memoir of an Out-of-Sight Mathematician, Mathematical Association of America, Washington, DC, 2012, 206 pp, by Larry Baggett., ISBN 978-0-88385-581-2, \$50} . . . . . . . . 91--92 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 93--94 Eric C. Chi and Kenneth Lange A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization . . . . . . . 95--108 Vincent Coll and Mike Harrison Two Generalizations of a Property of the Catenary . . . . . . . . . . . . . . . . 109--119 Pantelis A. Damianou A Beautiful Sine Formula . . . . . . . . 120--135 Ron Evans and Lihua Huang and Tuan Nguyen Keeler's Theorem and Products of Distinct Transpositions . . . . . . . . 136--144 Jaime Gaspar Non-recursive Polynomial Formula for the Sum of the Powers of the Integers . . . 144--144 David Grant The Quadratic Gauss Sum Redux . . . . . 145--149 Miles Dillon Edwards A Possibly New Proof of the Law of Cos 149--149 Yuly Billig and John D. Dixon An Eigenvalue Theorem for Systems of Polynomial Equations . . . . . . . . . . 150--153 Hongwei Lou A Short Proof of Stirling's Formula . . 154--157 Richard Ehrenborg Hamiltonian Cycles on Archimedean Solids Are Twisting Free . . . . . . . . . . . 158--161 Chua Cheong Siong A Simple Proof of Ljunggren's Binomial Congruence . . . . . . . . . . . . . . . 162--164 Daniel J. Velleman Monthly Gems . . . . . . . . . . . . . . 164--164 Peter J. McGrath Another Proof of Clairaut's Theorem . . 165--166 Hossein Hosseini Giv Proving the Banach--Alaoglu Theorem via the Existence of the Stone-\vCech Compactification . . . . . . . . . . . . 167--169 Anonymous Problems and Solutions . . . . . . . . . 170--177 Harold P. Boas Book Review: \booktitleInvitation to Classical Analysis, American Mathematical Society, Providence, RI, 2012, xiii + 392 pp, by Peter Duren., ISBN 978-0-8218-6932-1, \$74.00} . . . . 178--182 Peter D. Lax Book Review: \booktitleNumbers and Functions: From a Classical Experimental Mathematicians Point of View, American Mathematical Society, Providence, RI, 2012, 504 pp, by Victor H. Moll., ISBN 978-0-8218-8795-0, \$58} . . . . . . . . 183--183 Anonymous Back Matter . . . . . . . . . . . . . . 184--184
Anonymous Front Matter . . . . . . . . . . . . . . 185--186 Kenneth A. Ross and Ann E. Watkins Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2014 to Joan Leitzel for Distinguished Service to Mathematics . . 187--190 David H. Bailey and Jonathan Borwein Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal . . . . . . . . 191--206 Stephan Berendonk The Length of Spirographic Curves . . . 207--212 Alec S. Cooper and Oleg Pikhurko and John R. Schmitt and Gregory S. Warrington Martin Gardner's Minimum No-$3$-in-a-Line Problem . . . . . . . . 213--221 Aleksander Maliszewski and Marcin Szyszkowski Level Sets on Disks . . . . . . . . . . 222--228 Junesang Choi and Hari M. Srivastava Series Involving the Zeta Functions and a Family of Generalized Goldbach--Euler Series . . . . . . . . . . . . . . . . . 229--236 B. Sury A Polynomial Parent to a Fibonacci--Lucas Relation . . . . . . . 236--236 Trevor Hyde A Wallis Product on Clovers . . . . . . 237--243 Mircea Merca On Some Power Sums of Sine or Cosine . . 244--248 William Johnston The Weighted Hermite Polynomials Form a Basis for $ L_2 (\mathbb {R}) $ . . . . 249--253 Gerd Herzog A Proof of Lie's Product Formula . . . . 254--257 Kenneth Lange Hadamard's Determinant Inequality . . . 258--259 S. Koçak and M. Limoncu Mean of the Mean of the Mean \ldots . . 259--259 Justin Tatch Moore Justin Tatch Moore . . . . . . . . . . . 260--262 Marc Chamberland and Doron Zeilberger A Short Proof of McDougall's Circle Theorem . . . . . . . . . . . . . . . . 263--265 Anonymous Problems and Solutions . . . . . . . . . 266--273 Mark Kozek Book Review: \booktitleMathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media. Edited by Jessica K. Sklar and Elizabeth S. Sklar; Foreword by Keith Devlin. McFarland, Jefferson, NC, 2012, viii + 345 pp., ISBN 978-0-7864-4978-1, \$45} . . . . . . . . 274--278 Anonymous Back Matter . . . . . . . . . . . . . . 279--280
Anonymous Front Matter . . . . . . . . . . . . . . 281--282 Andrew J. Simoson Periodicity Domains and the Transit of Venus . . . . . . . . . . . . . . . . . 283--298 Daniel J. Velleman A Drug-Induced Random Walk . . . . . . . 299--317 Alexei Yu. Uteshev Analytical Solution for the Generalized Fermat--Torricelli Problem . . . . . . . 318--331 Samuel J. Ferguson A One-Sentence Line-of-Sight Proof of the Extreme Value Theorem . . . . . . . 331--331 Martin Kovár and Alena Chernikava On the Proof of the Existence of Undominated Strategies in Normal Form Games . . . . . . . . . . . . . . . . . 332--337 Chao-Ping Chen and Junesang Choi An Asymptotic Formula for $ (1 + 1 / x)^x $ Based on the Partition Function 338--343 Steffen Eger Stirling's Approximation for Central Extended Binomial Coefficients . . . . . 344--349 Thorsten Neuschel A New Proof of Stirling's Formula . . . 350--352 Ralph M. Krause Zeta(2) Once Again . . . . . . . . . . . 353--354 Andrea M. Hyde and Paul D. Lee and Blair K. Spearman Polynomials $ (x^3 - n)(x^2 + 3) $ Solvable Modulo Any Integer . . . . . . 355--358 B. Sury Macaulay Expansion . . . . . . . . . . . 359--360 J. J. Koliha Evaluating Lebesgue Integrals Efficiently with the FTC . . . . . . . . 361--364 Anonymous Problems and Solutions . . . . . . . . . 365--372 Jeffrey Nunemacher Book Review: \booktitleEncounters with Chaos and Fractals, 2nd edition. By Denny Gulick. Chapman and Hall/CRC Press, Boca Raton, 2012, xvi + 371 pp., ISBN 978-1-58488-517-7, \$79.95} . . . . 373--376 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 377--378 Allison Henrich and Louis H. Kauffman Unknotting Unknots . . . . . . . . . . . 379--390 Alan F. Beardon and Ian Short A Geometric Representation of Continued Fractions . . . . . . . . . . . . . . . 391--402 Tom Leinster Rethinking Set Theory . . . . . . . . . 403--415 Allan J. Kroopnick An Elementary Application of Brouwer's Fixed Point Theorem to Transition Matrices . . . . . . . . . . . . . . . . 415--415 Jon Grantham and Witold Jarnicki and John Rickert and Stan Wagon Repeatedly Appending Any Digit to Generate Composite Numbers . . . . . . . 416--421 Iddo Ben-Ari and Diana Hay and Alexander Roitershtein On Wallis-type Products and Pólya's Urn Schemes . . . . . . . . . . . . . . . . 422--432 Paul Pollack and Enrique Treviño The Primes that Euclid Forgot . . . . . 433--437 Emmanuel Tsukerman Solution of Sondow's Problem: A Synthetic Proof of the Tangency Property of the Parbelos . . . . . . . . . . . . 438--443 José Ángel Cid Araújo A Difference Equation Leading to the Irrationality of $ \surd 2 $ . . . . . . 443--443 Nathan A. Carlson A Connection between Furstenberg's and Euclid's Proofs of the Infinitude of Primes . . . . . . . . . . . . . . . . . 444--444 Ming-Chia Li An Elementary Proof of a Generalization of Banach's Mapping Theorem . . . . . . 445--446 M. L. Glasser A Technique in Contour Integration . . . 447--448 Kyle Luh and Nicholas Pippenger Large-Deviation Bounds for Sampling without Replacement . . . . . . . . . . 449--454 Anonymous Problems and Solutions . . . . . . . . . 455--462 Daniel Ullman Book Review: \booktitleMath on Trial: How Mathematics Is Used and Abused in the Courtroom, By Leila Schneps and Coralie Colmez, Basic Books, New York, 2013, xi + 256 pp., ISBN 978-0-465-03292-1, \$26.99} . . . . . . 463--466 Anonymous Editor's Endnotes . . . . . . . . . . . 467--468 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 469--470 Alberto Facchini and Giulia Simonetta Rational Numbers, Finite Cyclic Monoids, Divisibility Rules, and Numbers of Type $ 99 \cdots {} 900 \cdots {} 0 $ . . . . 471--485 David Borwein and Jonathan M. Borwein and Brailey Sims On the Solution of Linear Mean Recurrences . . . . . . . . . . . . . . 486--498 Josef Rukavicka Rejection of Laplace's Demon . . . . . . 498--498 C. W. Groetsch and S. A. Yost Vertical Projection in a Resisting Medium: Reflections on Observations of Mersenne . . . . . . . . . . . . . . . . 499--505 J. Scott Carter and Daniel S. Silver and Susan G. Williams Three Dimensions of Knot Coloring . . . 506--514 Harris Kwong An Alternate Proof of Sury's Fibonacci--Lucas Relation . . . . . . . 514--514 Jose Pujol On Hamilton's Nearly-Forgotten Early Work on the Relation between Rotations and Quaternions and on the Composition of Rotations . . . . . . . . . . . . . . 515--522 B. Sury A Heuristic Argument for Hua's Identity Using Geometric Series . . . . . . . . . 522--522 Tommy Wright Lagrange's Identity and Congressional Apportionment . . . . . . . . . . . . . 523--528 Chai Wah Wu Pigeonholes and Repunits . . . . . . . . 529--533 Kevin K. Ferland Record Crossword Puzzles . . . . . . . . 534--536 Michael Z. Spivey A Combinatorial Proof for the Alternating Convolution of the Central Binomial Coefficients . . . . . . . . . 537--540 Nikolai Nikolov and Blagovest Sendov A Converse of the Gauss--Lucas Theorem 541--544 Yared Nigussie Finding Your Seat Versus Tossing a Coin 545--546 Erich Badertscher A Simple Direct Proof of Marden's Theorem . . . . . . . . . . . . . . . . 547--548 Anonymous Problems and Solutions . . . . . . . . . 549--556 James A. Swenson Book Review: \booktitleWhich Numbers Are Real?, By Michael Henle. Mathematical Association of America, Washington, DC, 2012, x + 219 pp., ISBN 978-0-88385-777-9, \$53.00} . . . . . . 557--560 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 561--562 Erwan Brugallé and Kristin Shaw A Bit of Tropical Geometry . . . . . . . 563--589 Marcelo Brafman Another Algebraic Pythagorean Proof . . 589--589 Bryan Brown and Michael Dairyko and Stephan Ramon Garcia and Bob Lutz and Michael Someck Four Quotient Set Gems . . . . . . . . . 590--598 Vinícius G. Pereira de Sá and Celina M. H. de Figueiredo Blind-friendly von Neumann's Heads or Tails . . . . . . . . . . . . . . . . . 600--609 Richard Katz and Mike Krebs and Anthony Shaheen Zero Sums on Unit Square Vertex Sets and Plane Colorings . . . . . . . . . . . . 610--618 D. Zagier A Refinement of a Theorem of J. E. Littlewood . . . . . . . . . . . . . . . 618--618 Rajendra Bhatia and Rajesh Sharma Positive Linear Maps and Spreads of Matrices . . . . . . . . . . . . . . . . 619--624 Wen D. Chang and Russell A. Gordon Trisecting Angles in Pythagorean Triangles . . . . . . . . . . . . . . . 625--631 Diego Marques Yet Another Direct Proof of the Uncountability of the Transcendental Numbers . . . . . . . . . . . . . . . . 631--631 Rom Pinchasi Points Covered an Odd Number of Times by Translates . . . . . . . . . . . . . . . 632--636 Meinolf Geck On the Characterization of Galois Extensions . . . . . . . . . . . . . . . 637--639 Samuel G. Moreno and Esther M. García-Caballero Simpson's Rule and Sums of Powers . . . 639--639 F. Dreher and T. Samuel Continuous Images of Cantor's Ternary Set . . . . . . . . . . . . . . . . . . 640--643 Robert A. Beezer Extended Echelon Form and Four Subspaces 644--647 Anonymous Problems and Solutions . . . . . . . . . 648--657 Michael Barr Book Review: \booktitleThe Outer Limits of Reason, Noson Yanofsky. MIT Press, Cambridge, MA and London, England, 2013, xiv + 403 pp., ISBN 978-0-262-01935-4, \$29.95} . . . . . . . . . . . . . . . . 658--660 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 659--662 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Fourth William Lowell Putnam Mathematical Competition . . . . . . . . 663--673 Persi Diaconis and Xuancheng Shao and Kannan Soundararajan Carries, Group Theory, and Additive Combinatorics . . . . . . . . . . . . . 674--688 Marc Deléglise and Andrew Markoe On the Maximum Arc Length of Monotonic Functions . . . . . . . . . . . . . . . 689--699 David Borwein and Jonathan Borwein Deriving New Sinc Results from Old . . . 700--705 Michael Joswig and Günter M. Ziegler Foldable Triangulations of Lattice Polygons . . . . . . . . . . . . . . . . 706--710 Jonathan Novak Pólya's Random Walk Theorem . . . . . . . 711--716 Michael Schramm and John Troutman and Daniel Waterman Segmentally Alternating Series . . . . . 717--722 John Molokach Law of Cosines --- A Proof Without Words 722--722 Mark H. Holmes Connections Between Cubic Splines and Quadrature Rules . . . . . . . . . . . . 723--726 M. Scott Osborne Hausdorffization and Such . . . . . . . 727--733 Donald M. Davis Binomial Coefficients Involving Infinite Powers of Primes . . . . . . . . . . . . 734--737 Anonymous Problems and Solutions . . . . . . . . . 738--745 Brian M. Loft Book Review: \booktitleThe Cult of Pythagorus: Math and Myths, by Alberto A. Martínez. University of Pittsburgh Press, Pittsburgh, PA, 2012, xxii + 264 pp., ISBN 978-0-8229-4418-8, \$27.95} 746--748 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 747--750 Anonymous Front Matter . . . . . . . . . . . . . . 747--750 Fred Adler and Elizabeth S. Allman and Lisette G. de Pillis A Letter from the Guest Editors . . . . 751--753 Jonathan R. Potts and Mark A. Lewis A Mathematical Approach to Territorial Pattern Formation . . . . . . . . . . . 754--770 Mike Steel Tracing Evolutionary Links between Species . . . . . . . . . . . . . . . . 771--792 Roderick Edwards and Leon Glass Dynamics in Genetic Networks . . . . . . 793--809 Hoa Nguyen and Ricardo Cortez and Lisa Fauci Computing Flows Around Microorganisms: Slender-Body Theory and Beyond . . . . . 810--823 David Terman Mathematical Neuroscience . . . . . . . 824--839 Trachette Jackson and Natalia Komarova and Kristin Swanson Mathematical Oncology: Using Mathematics to Enable Cancer Discoveries . . . . . . 840--856 Laurie J. Heyer and Jeffrey L. Poet Synthetic Biology: A New Frontier . . . 857--867 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 867--870 Anonymous Front Matter . . . . . . . . . . . . . . 867--870 Peter J. Giblin and J. Paul Warder Evolving Evolutoids . . . . . . . . . . 871--889 Pieter Moree Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers . . . 890--902 Lei Ni A Perron-type Theorem on the Principal Eigenvalue of Nonsymmetric Elliptic Operators . . . . . . . . . . . . . . . 903--908 Pete L. Clark and Niels J. Diepeveen Absolute Convergence in Ordered Fields 909--916 William F. Trench An Unnoticed Consequence of Szeg\Ho's Distribution Theorem . . . . . . . . . . 917--921 Jack Button and Maurice Chiodo and Mariano Zeron-Medina Laris Coset Intersection Graphs for Groups . . 922--926 Sam Northshield Complex Descartes Circle Theorem . . . . 927--931 Pallab Kanti Dey and R. Thangadurai The Length of an Arithmetic Progression Represented by a Binary Quadratic Form 932--936 Marshall Hampton Cosines and Cayley, Triangles and Tetrahedra . . . . . . . . . . . . . . . 937--941 Felipe Acker A Note on the Spectral Theorem in the Finite-Dimensional Real Case . . . . . . 942--945 Anonymous Problems and Solutions . . . . . . . . . 946--953 Anonymous Problems and Solutions . . . . . . . . . 946--953 Genevieve S. Walsh Book Review: \booktitleMostly Surfaces, By Richard Evan Schwartz. American Mathematical Society, Providence, RI, 2010, xiii + 314 pp., ISBN 978-0-8218-5368-9, \$47.00} . . . . . . 954--956 Anonymous Editor's Endnotes . . . . . . . . . . . 957--959 Anonymous Monthly Referees for 2014 . . . . . . . 960--962 Jonathan Sondow From the \booktitleMonthly Over 100 Years Ago \ldots . . . . . . . . . . . . 963--963 Jonathan Sondow From the Monthly Over 100 Years Ago\ldots . . . . . . . . . . . . . . . 963--963 Amrik Singh Nimbran One More Proof of the Irrationality of $ \sqrt 2 $ . . . . . . . . . . . . . . . 964--964 Anonymous Back Matter . . . . . . . . . . . . . . ?? Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Scott T. Chapman A Letter from the Editor: 2015 is the Centennial Year of the MAA . . . . . . . 3--3 David E. Zitarelli The First 100 Years of the MAA . . . . . 4--23 Frank Swenton Simultaneous Proof of the First Fundamental Theorem of Calculus and Integrability of Continuous Functions 23--23 Titu Andreescu and Vladimir Georgiev and Oleg Mushkarov and Vladimir Georgiev and Oleg Mushkarov Napoleon Polygons . . . . . . . . . . . 24--29 Kenneth S. Williams Historical Remark on Ramanujan's Tau Function . . . . . . . . . . . . . . . . 30--35 Branko \'Curgus and Robert I. Jewett and Robert I. Jewett Somewhat Stochastic Matrices . . . . . . 36--42 Michael Hardy Stereographic Trigonometric Identities 43--47 Xianzu Lin Infinitely Many Primes in the Arithmetic Progression $ k n - 1 $ . . . . . . . . 48--51 P. Mark Kayll Deranged Matchings: Enumeration by Integration!! . . . . . . . . . . . . . 51--51 Francis C. Motta and Patrick D. Shipman and Bethany Springer A Point of Tangency Between Combinatorics and Differential Geometry 52--55 Hossein Hosseini Giv The Axiom of Choice, Well-Ordering, and Well-Classification . . . . . . . . . . 56--59 R. Ehrenhorg An Unbiased Marriage Theorem . . . . . . 59--59 Ignacio Ojeda Kronecker Square Roots and the Block Vec Matrix . . . . . . . . . . . . . . . . . 60--64 Pablo A. Panzone On a Formula of S. Ramanujan . . . . . . 65--69 Edward S. Letzter Continuity is an Adjoint Functor . . . . 70--74 Anonymous Problems and Solutions . . . . . . . . . 75--82 Edward F. Schaefer Book Review: \booktitleThe Mathematics of Encryption: An Elementary Introduction, Reviewed work(s): The Mathematics of Encryption: An Elementary Introduction. By Margaret Cozzens and Steven J. Miller. American Mathematical Society, Providence, RI, 2013, xviii + 332 pp., ISBN 978-0-8218-8321-1, \$49.00} . . . . . . . . . . . . . . . . 83--88 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 87--90 Yves Nievergelt Backward Analysis Explained with Monthly Payments . . . . . . . . . . . . . . . . 91--120 Christopher O'Neill and Roberto Pelayo and Roberto Pelayo How Do You Measure Primality? . . . . . 121--137 Aydin Shukurov The Power System is Never a Basis in the Space of Continuous Functions . . . . . 137--137 Carlos A. Catalá de la Torre A New Proof for a Sharp van der Corput's Lemma . . . . . . . . . . . . . . . . . 138--142 S. Koçak Dihedral Angles of the Regular $n$-Simplex . . . . . . . . . . . . . . 143--143 Arseniy V. Akopyan Geometry of the Cardioid . . . . . . . . 144--150 Marcelo Brafman Another Algebraic Pythagorean Proof . . 150--150 G. Molinari Elementary Prime Identities . . . . . . 151--154 Joachim Gräter and Karl-Joachim Wirths and Karl-Joachim Wirths On Elementary Bounds for $ \sum \nolimits_{k = n}^\infty {k^{-s}} $ . . 155--158 Paul Pollack An Easy Generalization of Euler's Theorem on the Series of Prime Reciprocals . . . . . . . . . . . . . . 159--163 Daniel Drucker A Comprehensive Pythagorean Theorem for all Dimensions . . . . . . . . . . . . . 164--168 Samuel G. Moreno and Esther M. García-Caballero A Geometric Proof of Morrie's Law . . . 168--168 Bao Qin Li Two Elementary Properties of Entire Functions . . . . . . . . . . . . . . . 169--172 Xiongping Dai From the First Borel--Cantelli Lemma to Poincaré's Recurrence Theorem . . . . . . 173--174 Anonymous Problems and Solutions . . . . . . . . . 175--182 Gerald B. Folland Book Review: \booktitleHidden Harmony---Geometric Fantasies: The Rise of Complex Function Theory, By Umberto Bottazzini and Jeremy Gray. Springer, New York, 2013, xvii + 848 pp., ISBN 978-1-4614-5724-4, \$189.00 (hardcover), ISBN 978-1-4614-5725-1, \$149.00 (eBook) 183--188 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 189--190 Jennifer J. Quinn Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2015 to W. James Lewis for Distinguished Service to Mathematics . . 191--194 Jonathan M. Borwein and Scott T. Chapman I Prefer Pi: a Brief History and Anthology of Articles in the \booktitleAmerican Mathematical Monthly 195--216 David Peifer Max Dehn and the Origins of Topology and Infinite Group Theory . . . . . . . . . 217--233 Samuel G. Moreno and Esther M. García-Caballero A Geometric Proof of Morrie's Law . . . 233--233 Jaap Eising and David Radcliffe and Jaap Top A Simple Answer to Gelfand's Question 234--245 Doreen De Leon Using Undetermined Coefficients to Solve Certain Classes of Variable-Coefficient Equations . . . . . . . . . . . . . . . 246--255 Matthias Beck and Neville Robbins Variations on a Generating-Function Theme: Enumerating Compositions with Parts Avoiding an Arithmetic Sequence 256--263 Anton Petrunin Area Minimizing Polyhedral Surfaces are Saddle . . . . . . . . . . . . . . . . . 264--267 William Goldbloom Bloch Open Discontinuous Maps From $ \mathbb {R}^n $ onto $ \mathbb {R}^n $ . . . . . 268--271 Mizan R. Khan and Richard Magner An Application of Modular Hyperbolas to Quadratic Residues . . . . . . . . . . . 272--274 Marius Tarnauceanu Finite Groups With a Certain Number of Cyclic Subgroups . . . . . . . . . . . . 275--276 John Konvalina Powers of Matrices and Algebraic Centrosymmetry . . . . . . . . . . . . . 277--279 Peter Horak Partitioning $ \mathbb {R}^n $ into Connected Components . . . . . . . . . . 280--283 Konstantinos Gaitanas An Explicit Formula for the Prime Counting Function Which is Valid Infinitely Often . . . . . . . . . . . . 283--283 Anonymous Problems and Solutions . . . . . . . . . 284--291 Reuben Hersh Book Review: \booktitleHow Humans Learn to Think Mathematically. Exploring the Three Worlds of Mathematics . . . . . . 292--296 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 297--298 Richard Montgomery The Three-Body Problem and the Shape Sphere . . . . . . . . . . . . . . . . . 299--321 Rebekah Ann Gilbert A Fine Rediscovery . . . . . . . . . . . 322--331 Juliá Cufí and Agustí Reventó and Carlos J. RodrÍz Curvature for Polygons . . . . . . . . . 332--337 Karl Dilcher and Larry Ericksen The Polynomials of Mahler and Roots of Unity . . . . . . . . . . . . . . . . . 338--353 Altino F. Santos A New Metric on Spherical $f$-Tilings 354--361 Patrick M. Fitzpatrick and Brian R. Hunt Absolute Continuity of a Function and Uniform Integrability of Its Divided Differences . . . . . . . . . . . . . . 362--366 Vadim Ponomarenko A Base Conversion Surprise . . . . . . . 366 402--366 Michal Adamaszek Face Numbers of Down-Sets . . . . . . . 367--370 Dirk Huylebrouck Generalizing Wallis' Formula . . . . . . 371--372 Mehmet Kilic A New Geometric Proof for Morley's Theorem . . . . . . . . . . . . . . . . 373--376 Hidefumi Katsuura A New Infinite Series Representation of $ \ln k $ . . . . . . . . . . . . . . . 376--376 Maxim Arnold and Vadim Zharnitsky Cyclic Evasion in the Three Bug Problem 377--380 \Ethorde Barali\'c A Short Proof of the Bradley Theorem . . 381--385 Byron Schmuland Linear Recurrences via Probability . . . 386--389 Anonymous Problems and Solutions . . . . . . . . . 390--397 Will Traves Book Review: \booktitlePerspectives in Projective Geometry. A Guided Tour Through Real and Complex Geometry . . . 398--402 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 405--406 Donald G. Saari Mathematics and the ``Dark Matter'' Puzzle . . . . . . . . . . . . . . . . . 407--423 Alex Chin and Gary Gordon and Kellie MacPhee and Charles Vincent Pick a Tree --- Any Tree . . . . . . . . 424--432 Christian Aebi and Grant Cairns Generalizations of Wilson's Theorem for Double-, Hyper-, Sub- and Superfactorials . . . . . . . . . . . . 433--443 Óscar Ciaurri and Luis M. Navas and Francisco J. Ruiz and Juan L. Varona A Simple Computation of $ \zeta (2 k) $ 444--451 Nam Gu Heo A New Proof of the Pythagorean Theorem 451--451 Jeffrey A. Boyle Using Rolling Circles to Generate Caustic Envelopes Resulting from Reflected Light . . . . . . . . . . . . 452--466 Sam Northshield A One-Line Proof of the Infinitude of Primes . . . . . . . . . . . . . . . . . 466--466 Ivan Izmestiev A Porism for Cyclic Quadrilaterals, Butterfly Theorems, and Hyperbolic Geometry . . . . . . . . . . . . . . . . 467--475 Maria Bras-Amorós and Marta Pujol Side Lengths of Equiangular Polygons (as seen by a coding theorist) . . . . . . . 476--478 Iosif Pinelis Relationships Between the First Four Moments . . . . . . . . . . . . . . . . 479--481 Janusz Januszewski An Upper Bound for Some Coloring Problem 481--481 Meinolf Geck Eigenvalues of Real Symmetric Matrices 482--483 Bogdan Veklych A One-Formula Proof of the Nonvanishing of $L$-Functions of Real Characters at $1$ . . . . . . . . . . . . . . . . . . 484--485 Jesús Jerónimo Castro The Volume of the Convex Hull of a Body and its Homothetic Copies . . . . . . . 486--489 J. Michael Steele Explaining a Mysterious Maximal Inequality --- and a Path to the Law of Large Numbers . . . . . . . . . . . . . 490--494 Michael Hardy Using Infinitesimals to Differentiate Secant and Tangent . . . . . . . . . . . 494--494 Ádám Besenyei The Brocard Angle and a Geometrical Gem from Dmitriev and Dynkin . . . . . . . . 495--499 Anonymous Problems and Solutions . . . . . . . . . 500--507 Gerald B. Folland Book Review: \booktitleA History in Sum: 150 Years of Mathematics at Harvard (1825--1975), By Steve Nadis and Shing-Tung Yau. Harvard University Press, Cambridge, 2013, xviii + 249 pp., ISBN 978-0-674-72500-3, \$39.95} . . . . 508--510 Anonymous Editor's Endnotes . . . . . . . . . . . 511--512 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 513--514 Dennis D. A. Epple and Jason Siefken Collapse: A Fibonacci and Sturmian Game 515--527 Kenneth S. Williams A ``Four Integers'' Theorem and a ``Five Integers'' Theorem . . . . . . . . . . . 528--536 Lorenz Halbeisen and Norbert Hungerbühler A Simple Proof of Poncelet's Theorem (on the Occasion of Its Bicentennial) . . . 537--551 Aaditya Salgarkar and Rishi Mehta Alternate Derivation for the Parity of the $ n^{\rm th} $ Triangular Number . . 551--551 Nicholas J. Werner Covering Numbers of Finite Rings . . . . 552--566 J. Rooin and A. Alikhani A Geometric Proof of the Beppo--Levi Inequality . . . . . . . . . . . . . . . 566--566 Alan Haynes and Sara Munday Diophantine Approximation and Coloring 567--580 Haryono Tandra A Proof of the Replacement Theorem by the Notion of Maximal Elements . . . . . 580--580 Satomi Murakami and Hiroki Ohwa Periodic Points of Some Discontinuous Mappings . . . . . . . . . . . . . . . . 581--586 Vadim Ponomarenko Asymptotic Formula for $ (1 + 1 / x)^x $, Revisited . . . . . . . . . . . . . . 587--587 Virgil Barnard A Proof of Quadratic Reciprocity . . . . 588--592 Daniel Daners Uniform Continuity of Continuous Functions on Compact Metric Spaces . . . 592--592 Iosif Pinelis On the Hölder and Cauchy--Schwarz Inequalities . . . . . . . . . . . . . . 593--595 José Gascón Another Proof That the Real Numbers $ \mathbb {R} $ Are Uncountable . . . . . 596--597 Haryono Tandra A Simple Modified Version for Ferguson's Proof of the Extreme Value Theorem . . . 598--598 Mircea Merca An Alternative to Faulhaber's Formula 599--601 Tommaso Drammatico A New Proof of the Equality of Mixed Second Partial Derivatives . . . . . . . 602--603 Anonymous Problems and Solutions . . . . . . . . . 604--612 Marion Cohen Book Review: \booktitleMathematicians on Creativity. Edited by Peter B. Borwein, Peter Liljedahl, and Helen Zhai, The Mathematical Association of America, Washington DC, 2014, xviii + 199 pp, ISBN 978-0-88385-574-4, \$30.00} . . . . 613--616 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 616--618 Manya Raman-Sundström A Pedagogical History of Compactness . . 619--635 Carl Pomerance Divisors of the Middle Binomial Coefficient . . . . . . . . . . . . . . 636--644 Neil Ashby Isosynchronous Paths on a Rotating Surface . . . . . . . . . . . . . . . . 645--659 Matthias Beck and Ana Berrizbeitia and Michael Dairyko and Claudia Rodriguez and Amanda Ruiz and Schuyler Veeneman Parking Functions, Shi Arrangements, and Mixed Graphs . . . . . . . . . . . . . . 660--673 Pablo G. Barrientos A Family of Eventually Expanding Piecewise Linear Maps of the Interval 674--680 Robert Cowen Deleting Edges from Ramsey Minimal Examples . . . . . . . . . . . . . . . . 681--683 Diego Marques A New Fibonacci--Lucas Relation . . . . 683--683 Hans J. H. Tuenter A Double Binomial Sum: Putnam $ 35$-A4 Revisited . . . . . . . . . . . . . . . 684--689 Michael D. Hirschhorn Wallis's Product and the Central Binomial Coefficient . . . . . . . . . . 689--689 James E. McClure and Alec McGail An Elementary Treatment of the Construction of the Free Product of Groups . . . . . . . . . . . . . . . . . 690--692 Óscar Ciaurri Euler's Product Expansion for the Sine: An Elementary Proof . . . . . . . . . . 693--695 Edward Omey On Xiang's Observations Concerning the Cauchy--Schwarz Inequality . . . . . . . 696--698 Samuel G. Moreno The Dramatic and Ultimate Shortening of a Doctoral Dissertation in Mathematics 699--699 Anonymous Problems and Solutions . . . . . . . . . 700--707 Joseph Malkevitch Book Review: \booktitleThe Mathematical Coloring Book . . . . . . . . . . . . . 708--712 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 713--714 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Fifth William Lowell Putnam Mathematical Competition . . . . . . . . 715--725 California Jack Cassidy Early Round Bluffing in Poker . . . . . 726--744 Tom M. Apostol and Mamikon A. Mnatsakanian Volume/Surface Area Relations for $n$-Dimensional Spheres, Pseudospheres, and Catenoids . . . . . . . . . . . . . 745--756 P. Pollack and J. Vandehey Besicovitch, Bisection, and the Normality of $ 0. (1)(4)(9)(16)(25) $ 757--765 Shui-Hung Hou and Edwin Hou On a Recursion Formula Related to Confluent Vandermonde . . . . . . . . . 766--772 Syahida Che Dzul-Kifli and Chris Good On Devaney Chaos and Dense Periodic Points: Period $3$ and Higher Implies Chaos . . . . . . . . . . . . . . . . . 773--780 Cristinel Mortici Funny Forms of the Mean Value Theorem 780--780 Tadashi Tokieda A Viscosity Proof of the Cauchy--Schwarz Inequality . . . . . . . . . . . . . . . 781--781 Tomasz Kania A Short Proof of the Fact That the Matrix Trace Is the Expectation of the Numerical Values . . . . . . . . . . . . 782--783 Levent Alpoge van der Waerden and the Primes . . . . . 784--785 Raphaël Cerf and Matthias Gorny An Exponential Inequality for Symmetric Random Variables . . . . . . . . . . . . 786--789 Melvyn B. Nathanson Pairs of Matrices in $ {\rm GL}_2 (R_{\geq 0}) $ That Freely Generate . . 790--792 Zsolt Lengvárszky Pythagoras by Integral . . . . . . . . . 792--792 Tamás Titkos A Simple Proof of the Lebesgue Decomposition Theorem . . . . . . . . . 793--794 Haryono Tandra A New Proof of the Change of Variable Theorem for the Riemann Integral . . . . 795--799 Jonathan M. Borwein and Scott T. Chapman I Prefer Pi: Addenda . . . . . . . . . . 800--800 Anonymous Problems and Solutions . . . . . . . . . 801--808 Ferebee Tunno Book Review: \booktitleReviews . . . . . 809--812 Tamás Titkos How to Make Equivalent Measures? . . . . 812--812 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 813--814 Zhiqin Lu and Julie Rowlett The Sound of Symmetry . . . . . . . . . 815--835 Péter Hajnal and László I. Szabó and Vilmos Totik Convex Polygons and Common Transversals 836--844 Titu Andreescu and Vladimir Georgiev and Oleg Mushkarov Correction to ''Napoleon Polygons'' . . 844--844 Qingchun Ren and Jürgen Richter-Gebert and Bernd Sturmfels Cayley--Bacharach Formulas . . . . . . . 845--854 J. Roberto Hasfura-Buenaga Kronecker's Diophantine Approximation and the Asymptotics of Solutions of Difference Equations . . . . . . . . . . 855--861 Zbigniew Nitecki Cantorvals and Subsum Sets of Null Sequences . . . . . . . . . . . . . . . 862--870 Robert O. Stanton Sets Closed Under the Division Algorithm 871--879 George E. Andrews and Aviezri S. Fraenkel and James A. Sellers Characterizing the Number of $m$-ary Partitions Modulo $m$ . . . . . . . . . 880--885 Thomas J. Osler A Product of Nested Radicals for the AGM 886--887 Rafael de la Llave Computing Some Integrals by Computing Derivatives . . . . . . . . . . . . . . 888--889 Dmitry Ryabogin A Lemma of Nakajima and Süss on Convex Bodies . . . . . . . . . . . . . . . . . 890--892 Elias Lampakis A New Proof of Euler's Inequality . . . 892--892 Nguyen S. Hoang A Limit Comparison Test for General Series . . . . . . . . . . . . . . . . . 893--896 Hamid Reza Daneshpajouh A New Proof of $ \aleph_0$-Resolvability of a Metric Space Without an Isolated Point . . . . . . . . . . . . . . . . . 897--898 Anonymous Problems and Solutions . . . . . . . . . 899--906 Robin Hartshorne Book Review: \booktitleReviews . . . . . 907--911 Michael Henle Book Review: \booktitleReviews . . . . . 912--915 Anonymous Statement of Ownership . . . . . . . . . 916--916 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 917--918 Zhaiming Shen and Lasse Rempe-Gillen The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics 919--940 Fred Kuczmarski and James Kuczmarski Hanging Around in Non-Uniform Fields . . 941--957 Andrzej Nowicki Strong Divisibility and LCM-Sequences 958--966 Jesús Jerónimo Castro On Convex Curves Which Have Many Inscribed Triangles of Maximum Area . . 967--971 Sebastian M. Cioaba and Peter J. Cameron A Graph Partition Problem . . . . . . . 972--982 Jaime Gaspar All Triangles at Once . . . . . . . . . 982--982 Guram Bezhanishvili and David Pengelley What Does ``Less Than or Equal'' Really Mean? . . . . . . . . . . . . . . . . . 983--989 Haryono Tandra A Simple Proof of the Uniform Continuity of Real-Valued Continuous Functions on Compact Intervals . . . . . . . . . . . 989--989 Mehmet Kiliç and Sahin Koçak On Products of Uniquely Geodesic Spaces 990--994 Sadi Abu-Saymeh and Mowaffaq Hajja and Hellmuth Stachel Equicevian Points of a Triangle . . . . 995--1000 Weimin Peng A Generalized Liouville Theorem for Entire Functions . . . . . . . . . . . . 1001--1002 Atsushi Yamamori Yet Another Proof of Poincaré's Theorem 1003--1004 Kenneth Lange Polya's Random Walk Theorem Revisited 1005--1007 José Luis Cereceda Newton's Interpolation Polynomial for the Sums of Powers of Integers . . . . . 1007--1007 Jun-Ming Zhu A Semi-Finite Proof of Jacobi's Triple Product Identity . . . . . . . . . . . . 1008--1009 Anonymous Problems and Solutions . . . . . . . . . 1010--1017 Michael Harris Book Review: \booktitleReviews . . . . . 1018--1022 Anonymous Editor's Endnotes . . . . . . . . . . . 1023--1025 Anonymous Monthly Referees for 2015 . . . . . . . 1026--1028 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Richard D. Neidinger A Fair-Bold Gambling Function Is Simply Singular . . . . . . . . . . . . . . . . 3--18 Adrien Kassel and David B. Wilson The Looping Rate and Sandpile Density of Planar Graphs . . . . . . . . . . . . . 19--39 J. Ángel Cid and Rodrigo López Pouso Integration by Parts and by Substitution Unified with Applications to Green's Theorem and Uniqueness for ODEs . . . . 40--52 M. Ram Murty and Chester Weatherby A Generalization of Euler's Theorem for $ \zeta (2 k) $ . . . . . . . . . . . . 53--65 Shivarajkumar Beyond Schur's Conjecture . . . . . . . 66--70 Yaroslav Shitov The Diameter of Chess Grows Exponentially . . . . . . . . . . . . . 71--77 Daniel J. Velleman Monthly Gems . . . . . . . . . . . . . . 77--77 Michael C. Slattery On a Property Motivated by Groups with a Specified Number of Subgroups . . . . . 78--81 Oleg Viro Pictorial Calculus for Isometries . . . 82--87 Konstantinos Gaitanas A Partial Solution of Representing $1$ as a Sum of $n$ Distinct Unit Fractions 87--87 David G. Radcliffe A Function That Is Surjective on Every Interval . . . . . . . . . . . . . . . . 88--89 Thomas Osler Iterations for the Lemniscate Constant Resembling the Archimedean Algorithm for Pi . . . . . . . . . . . . . . . . . . . 90--93 Kuldeep Kumar Kataria A Probabilistic Proof of the Multinomial Theorem . . . . . . . . . . . . . . . . 94--96 Xiaoxue Li A Synthetic Approach to a USAMO Problem 96--96 Anonymous Problems and Solutions . . . . . . . . . 97--105 Darren B. Glass Book Review: \booktitleReviews . . . . . 106--112 József Sándor A Note on the Logarithmic Mean . . . . . 112--112 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 113--114 Francis C. Motta and Patrick D. Shipman and Bethany D. Springer Optimally Topologically Transitive Orbits in Discrete Dynamical Systems . . 115--135 Ian Morrison and David Swinarski Can You Play a Fair Game of Craps with a Loaded Pair of Dice? . . . . . . . . . . 136--148 Deborah A. Kent and David J. Muraki A Geometric Solution of a Cubic by Omar Khayyam \ldots in Which Colored Diagrams Are Used Instead of Letters for the Greater Ease of Learners . . . . . . . . 149--160 Mariano Suárez-Álvarez Cyclic Extensions Are Radical . . . . . 160--160 Josh Hiller Old Friends in Unexpected Places: Pascal (and Other) Matrices in $ {\rm GL}_n(C) $ . . . . . . . . . . . . . . . . . . . 161--167 John Brillhart and Richard Blecksmith and Mike Decaro Using Conic Sections to Factor Integers 168--174 Michael Z. Spivey Probabilistic Proofs of a Binomial Identity, Its Inverse, and Generalizations . . . . . . . . . . . . 175--180 E. W. Dekking and F. M. Dekking Helge von Koch's Snowflake Curve Revisited . . . . . . . . . . . . . . . 181--184 Jonathan Baker Strong Convexity Does Not Imply Radial Unboundedness . . . . . . . . . . . . . 185--188 Xin-Jie Sun On Sums of Three Pentagonal Numbers . . 189--191 Jeffrey Lutgen A Combinatorial Proof of an Alternating Convolution Identity for Multichoose Numbers . . . . . . . . . . . . . . . . 192--196 Anonymous Problems and Solutions . . . . . . . . . 197--204 Jeffrey Nunemacher Book Review: \booktitleReviews . . . . . 205--208 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 209--210 Jennifer J. Quinn Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2016 to George Berzsenyi for Distinguished Service to Mathematics . . 211--213 Karen Hunger Parshall Mathematics and the Politics of Race: The Case of William Claytor (Ph.D., University of Pennsylvania, 1933) . . . 214--240 John P. Boyd Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis . . . . . . . . . . . . . . . . 241--257 Boris M. Bekker and Oleg A. Ivanov and Alexander S. Merkurjev Milnor's Lemma, Newton's Method, and Continued Fractions . . . . . . . . . . 258--266 Clark Kimberling and Kenneth B. Stolarsky Slow Beatty Sequences, Devious Convergence, and Partitional Divergence 267--273 Steve Butler and Ron Graham and Richard Stong Inserting Plus Signs and Adding . . . . 274--279 Tom Mertens and Jeff Weeks Electromagnetism in a Multiconnected Universe . . . . . . . . . . . . . . . . 280--286 Jeffrey S. Ovall The Laplacian and Mean and Extreme Values . . . . . . . . . . . . . . . . . 287--291 Peter McGrath On the Smooth Jordan Brouwer Separation Theorem . . . . . . . . . . . . . . . . 292--295 José L. Ramírez An Identity of Carlitz and Its Generalization . . . . . . . . . . . . . 295--295 Anonymous Problems and Solutions . . . . . . . . . 296--303 Craig H. Jackson Book Review: \booktitleReviews . . . . . 304--308 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 309--310 Paul-Jean Cahen and Jean-Luc Chabert What You Should Know About Integer-Valued Polynomials . . . . . . . 311--337 Keith Johnson and Kira Scheibelhut Rational Polynomials That Take Integer Values at the Fibonacci Numbers . . . . 338--346 Gary Brookfield Factoring Forms . . . . . . . . . . . . 347--362 Grant Cairns and Yuri Nikolayevsky and Gavin Rossiter Conewise Linear Periodic Maps of the Plane with Integer Coefficients . . . . 363--375 Mohamed Ayad and Omar Kihel and Jesse Larone When Does a Given Polynomial with Integer Coefficients Divide Another? . . 376--381 Neil J. Calkin and Beth Novick and Hayato Ushijima-Mwesigwa What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments . . . . . 382--386 Nuno Luzia A Proof of The Pythagorean Theorem After Descartes . . . . . . . . . . . . . . . 386--386 Ovidiu Costin and Neil Falkner and Jeffery D. McNeal Some Generalizations of the Riemann--Lebesgue Lemma . . . . . . . . 387--391 Peter S. Landweber and Emanuel A. Lazar and Neel Patel On Fiber Diameters of Continuous Maps 392--397 Daniel López-Aguayo Irrationality via Maximality . . . . . . 397--397 Dennis S. Bernstein and Khaled F. Aljanaideh and Arthur E. Frazho Laurent Series and $ l^p $ Sequences . . 398--398 Anonymous Problems and Solutions . . . . . . . . . 399--406 Thomas Garrity Book Review: \booktitleReviews . . . . . 407--412 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 413--414 Sòren Eilers The LEGO Counting Problem . . . . . . . 415--426 Harold P. Boas Mocposite Functions . . . . . . . . . . 427--438 Tom M. Apostol and Mamikon A. Mnatsakanian A New Look at Surfaces of Constant Curvature . . . . . . . . . . . . . . . 439--447 Jaime Cruz-Sampedro and Margarita Tetlalmatzi-Montiel Hardy's Reduction for a Class of Liouville Integrals of Elementary Functions . . . . . . . . . . . . . . . 448--470 Piotr Josevich An Alternative Approach to the Product Rule . . . . . . . . . . . . . . . . . . 470--470 G. L. Mullen and D. Panario and D. Thomson Fast and Simple Modular Interpolation Using Factorial Representation . . . . . 471--480 Iosif Pinelis On Measurable Semigroups in $R$ . . . . 481--481 Arseniy Sheydvasser A Corrigendum to Unreasonable Slightness 482--485 Karl Dilcher and Christophe Vignat Euler and the Strong Law of Small Numbers . . . . . . . . . . . . . . . . 486--490 Tim Hsu and San José Rational Nonaxis Points on the Unit Circle Have Irrational Angles . . . . . 490--490 Iosif Pinelis Explicit Additive Decomposition of Norms on $ R^2 $ . . . . . . . . . . . . . . . 491--496 Michael Gaul and Fred Kuczmarski Parabolas and Archimedes' $ 2 / 3$-Property . . . . . . . . . . . . . . 497--501 Peter McGrath An Extremely Short Proof of the Hairy Ball Theorem . . . . . . . . . . . . . . 502--503 Anonymous Problems and Solutions . . . . . . . . . 504--511 Gerald L. Alexanderson Book Review: \booktitleReviews . . . . . 512--514 Anonymous Editor's End Notes . . . . . . . . . . . 515--516 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 517--518 Jennifer M. Johnson and János Kollár Arcology . . . . . . . . . . . . . . . . 519--541 Steve Butler and Persi Diaconis and Ron Graham The Mathematics of the Flip and Horseshoe Shuffles . . . . . . . . . . . 542--556 Valerio De Angelis and Dominic Marcello Wilf's Conjecture . . . . . . . . . . . 557--573 F. Adrián F. Tojo A Hyperbolic Analog of the Phasor Addition Formula . . . . . . . . . . . . 574--582 Pablo A. Panzone Tiling the Plane with Different Hexagons and Triangles . . . . . . . . . . . . . 583--591 Franklin H. J. Kenter How to Win Your Betting Pool with Jensen's Inequality and the Law of Large Numbers . . . . . . . . . . . . . . . . 592--596 Erhan Gürel On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products . . . . . . . . . . . . . . . . 597--599 Hunter Swan Expected Number of Vertices of a Hypercube Slice . . . . . . . . . . . . 600--604 Peter McCauley Proofs Without Using Limits of Both Calculus Power Rules . . . . . . . . . . 604--604 Pham Duy Khanh and Marc Lassonde Quasiconvex Linear Perturbations and Convexity . . . . . . . . . . . . . . . 605--608 Ariel Amir and Mikhail Lemeshko and Tadashi Tokieda Surprises in Numerical Expressions of Physical Constants . . . . . . . . . . . 609--612 Anonymous Problems and Solutions . . . . . . . . . 613--620 Leslie Hogben and Mark Hunacek Book Review: \booktitleReviews . . . . . 621--624 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 625--626 Laura Florescu and Lionel Levine and Yuval Peres The Range of a Rotor Walk . . . . . . . 627--642 Lawrence Zalcman A Tale of Three Theorems . . . . . . . . 643--656 Márton Balázs and Áron Folly An Electric Network for Nonreversible Markov Chains . . . . . . . . . . . . . 657--682 Vincent E. Coll and Jeff Dodd A Characteristic Averaging Property of the Catenary . . . . . . . . . . . . . . 683--688 Dennis Ivanov and Serge Tabachnikov The Six Circles Theorem Revisited . . . 689--698 Arnon Avron and Nachum Dershowitz Cayley's Formula: A Page From The Book 699--700 Michael Hardy On Tangents and Secants of Infinite Sums 701--703 Alex Kasman Factorization of a Matrix Differential Operator Using Functions in Its Kernel 704--709 Brian D. Sittinger Computing $ \zeta (2 m) $ by using Telescoping Sums . . . . . . . . . . . . 710--715 Yuanyuan Yao and Wenxia Li Generating Iterated Function Systems for the Vicsek Snowflake and the Koch Curve 716--721 Anonymous Problems and Solutions . . . . . . . . . 722--730 Matthew Richey Book Review . . . . . . . . . . . . . . 731--736 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 737--738 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Sixth William Lowell Putnam Mathematical Competition . . . . . . . . 739--752 Jeffrey C. Lagarias Erd\Hos, Klarner, and the $ 3 x + 1 $ Problem . . . . . . . . . . . . . . . . 753--776 Dvij Bajpai and Daniel J. Velleman Anonymity in Predicting the Future . . . 777--788 Philippe Caldero and Jérôme Germoni Equilateral Triangles and the Fano Plane 789--801 T. S. Michael and Val Pinciu The Art Gallery Theorem, Revisited . . . 802--807 Lon Mitchell and Michael A. Jones and Brittany Shelton Abelian and Non-Abelian Triangle Mysteries . . . . . . . . . . . . . . . 808--813 Yong Kong and Shaowei Zhang The Adventitious Angles Problem: The Lonely Fractional Derived Angle . . . . 814--816 J. Jerónimo-Castro and C. Yee-Romero Maximal Isoptic Chords of Convex Curves 817--820 Olivier de La Grandville An Alternate Derivation of the Euler--Poisson Equation . . . . . . . . 821--824 J. A. Grzesik Yet Another Analytic Proof of Napoleon's Theorem . . . . . . . . . . . . . . . . 824--824 Bálint Farkas and Sven-Ake Wegner Variations on Barbalat's Lemma . . . . . 825--830 Anonymous Problems and Solutions . . . . . . . . . 831--839 Mark Kidwell Book Review . . . . . . . . . . . . . . 840--843 Halil Mutuk A Physical Proof for Cauchy's Inequality 843--843 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 845--846 Scott T. Chapman A Letter From the Editor: Jonathan M. Borwein (1951--2016) . . . . . . . . . . 847--848 Paul Baginski and Ryan Rodriguez and George J. Schaeffer and Yiwei She Finding Elements With Given Factorization Lengths and Multiplicities 849--870 Lyle Ramshaw Stråhle's Equal-Tempered Triumph . . . . 871--883 Jean C. Cortissoz A Note on Harmonic Functions on Surfaces 884--893 Uuganbaatar Ninjbat Another Memorable Mongolian Olympiad Problem: A Two-Colored Rectangular Lattice . . . . . . . . . . . . . . . . 894--899 Josh Brown Kramer and Jonathan Cutler and A. J. Radcliffe The Multistep Friendship Paradox . . . . 900--908 Sean Eastman and Selwyn Hollis and Kawee Numpacharoen and Jared Schlieper The Volume of the Spatial Region Corresponding to $ n \times n $ Correlation Matrices . . . . . . . . . . 909--918 Ivica Martinjak Two Extensions of the Sury's Identity 919--919 Bernd Schomburg Primitivity and Orbit Decomposition . . 920--923 Adrian W. Dudek On the Success of Mishandling Euclid's Lemma . . . . . . . . . . . . . . . . . 924--927 Alan J. Hoffman and Chai Wah Wu A Simple Proof of a Generalized Cauchy--Binet Theorem . . . . . . . . . 928--930 Nicolae Anghel Optimal Bounds for the Roots of Polynomials . . . . . . . . . . . . . . 931--935 Anthony J. Bevelacqua A Family of Non-Euclidean PIDs . . . . . 936--939 Kuldeep Kumar Kataria An Alternate Proof of the Binomial Theorem . . . . . . . . . . . . . . . . 940--940 Anonymous Problems and Solutions . . . . . . . . . 941--948 Gerald B. Folland Book Review . . . . . . . . . . . . . . 949--952 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 953--954 Scott T. Chapman A Letter from the Editor: The Long and Winding Road . . . . . . . . . . . . . . 955--958 Franco Bradshaw Single Digit NFL Scores . . . . . . . . 959--959 Alfred Geroldinger Sets of Lengths . . . . . . . . . . . . 960--988 Anton A. Klyachko and Anton N. Vassilyev Balanced Factorizations . . . . . . . . 989--1000 Melvyn B. Nathanson Cantor Polynomials and the Fueter--Pólya Theorem . . . . . . . . . . . . . . . . 1001--1012 Aaron M. Broussard and Martin E. Malandro and Abagayle Serreyn Optimizing the Video Game Multi-Jump: Player Strategy, AI, and Level Design 1013--1032 Jeffrey C. Lagarias and Takumi Murayama and D. Harry Richman Dilated Floor Functions That Commute . . 1033--1038 Stephan Ramon Garcia and Florian Luca Quotients of Fibonacci Numbers . . . . . 1039--1044 Richard Ehrenborg and Alex Happ Parking Cars of Different Sizes . . . . 1045--1048 Anonymous Corrigendum to ''A New Proof of the Change of Variable Theorem for the Riemann Integral'' . . . . . . . . . . . 1049--1049 Anonymous Problems and Solutions . . . . . . . . . 1050--1057 Chris A. Marx Book Review: \booktitleA First Course in the Calculus of Variations. By Mark Kot. Student Mathematical Library Vol 72, American Mathematical Society, Providence, Rhode Island, 2014, x + 298 pp., ISBN 978-1-4704-1495-5, \$50} . . . 1058--1061 Anonymous Monthly Referees for 2016 . . . . . . . 1062--1066 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 1--2 Susan Jane Colley Letter from the Editor . . . . . . . . . 3--3 Ryan Blair and Marion Campisi and Jesse Johnson and Scott A. Taylor and Maggy Tomova Neighbors of Knots in the Gordian Graph 4--23 Robert J. Vanderbei The Falling Slinky . . . . . . . . . . . 24--36 Antonio Cafure and Eda Cesaratto Irreducibility Criteria for Reciprocal Polynomials and Applications . . . . . . 37--53 Joseph A. Gallian Seventy-Five Years of the Putnam Mathematical Competition* . . . . . . . 54--59 Saveliy Ustuzhanin A Novel Way to Prove the Irrationality of $ \sqrt 2 $ . . . . . . . . . . . . . 59--59 Nicolae Anghel On a 2015 Putnam Problem Related to a Double Recursion . . . . . . . . . . . . 60--69 Ian Stewart Why Do All Triangles Form a Triangle? 70--73 Cezar Lupu A New Proof of the Finsler--Hadwiger Inequality . . . . . . . . . . . . . . . 73--73 Yusuf Z. Gürtas Chebyshev Polynomials and the Minimal Polynomial of $ \cos (2 \pi / n) $ . . . 74--78 Eli Shamir and Benny Sudakov Two-Sided, Unbiased Version of Hall's Marriage Theorem . . . . . . . . . . . . 79--80 Bart van Munster Hausdorffization and Homotopy . . . . . 81--82 Anonymous Problems and Solutions . . . . . . . . . 83--91 Jason Rosenhouse Reviews . . . . . . . . . . . . . . . . 92--95 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 98--98 Annalisa Crannell and Marc Frantz and Fumiko Futamura The Image of a Square . . . . . . . . . 99--115 Allen Stenger Experimental Math for Math Monthly Problems . . . . . . . . . . . . . . . . 116--131 Michael Maltenfort Characterizing Additive Systems . . . . 132--148 Bisharah Libbus and Gordon Simons and Yi-Ching Yao Rotating Multiple Sets of Labeled Points to Bring Them Into Close Coincidence: A Generalized Wahba Problem . . . . . . . 149--160 Scott Ginebaugh Generalized Infinite Products for Powers of $ e^{1 / k} $ . . . . . . . . . . . . 161--165 Christian Aebi and Grant Cairns Sums of Quadratic Residues and Nonresidues . . . . . . . . . . . . . . 166--169 Idris Mercer Another Proof That There Are Infinitely Many Primes . . . . . . . . . . . . . . 169--169 Chatchawan Panraksa and Pornrat Ruengrot A Note on Average of Roots of Unity . . 170--174 Charles Audet Maximal Area of Equilateral Small Polygons . . . . . . . . . . . . . . . . 175--178 Anonymous Problems and Solutions . . . . . . . . . 179--187 Alan Baker The Philosophies of Mathematics . . . . 188--192 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 194--194 Annalisa Crannell and Doug Ensley Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2017 to Martha Siegel for Distinguished Service to Mathematics . . 195--197 Pete L. Clark The Euclidean Criterion for Irreducibles 198--216 Joseph Bak and Strashimir G. Popvassilev The Evolution of Cauchy's Closed Curve Theorem and Newman's Simple Proof . . . 217--231 Jonathan Sondow and Kieren MacMillan Primary Pseudoperfect Numbers, Arithmetic Progressions, and the Erd\Hos--Moser Equation . . . . . . . . 232--240 Koji Momihara and Masashi Shinohara Distance Sets on Circles . . . . . . . . 241--254 Michael Weiss Where Are the Rational Squares? . . . . 255--259 Shubhodip Mondal Surjectivity of Maps Induced on Matrices by Polynomials and Entire Functions . . 260--264 Dirk Huylebrouck A New Regular (Compound) Polyhedron (of Infinite Kepler--Poinsot Type) . . . . . 265--268 Joseph Plante A Proof of Bonnet's Version of the Mean Value Theorem by Methods of Cauchy . . . 269--273 Anonymous Problems and Solutions . . . . . . . . . 274--281 Dominic Lanphier Book Review: \booktitleSumming it Up: From One Plus One to Modern Number Theory . . . . . . . . . . . . . . . . . 282--288 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 290--290 Paul E. Becker and Martin Derka and Sheridan Houghten and Jennifer Ulrich Build a Sporadic Group in Your Basement 291--305 John P. Boyd and Houjun Wang Convergent Power Series for Boundary Value Problems and Eigenproblems with Application to Atmospheric and Oceanic Tides . . . . . . . . . . . . . . . . . 306--323 Arno Berger More Grade School Triangles . . . . . . 324--336 Hiroshi Maehara and Horst Martini On Lexell's Theorem . . . . . . . . . . 337--344 Antonio Avilés and Grzegorz Plebanek A Little Ado about Rectangles . . . . . 345--350 Trevor D. Wooley A Superpowered Euclidean Prime Generator 351--352 Carl McTague On the Greatest Common Divisor of Binomial Coefficients . . . . . . . . . 353--356 Mehtaab S. Sawhney A Telescoping Proof of the AM--GM Inequality . . . . . . . . . . . . . . . 356--356 David E. Speyer A Counting Proof of a Theorem of Frobenius . . . . . . . . . . . . . . . 357--359 Evelyn R. Easdale and Jolene E. Fleming and Bogdan D. Suceava Convergence for Series With Terms Defined by a Recurrence Relation . . . . 360--364 Christian Elsholtz Golomb's Conjecture on Prime Gaps . . . 365--368 Anonymous Problems and Solutions . . . . . . . . . 369--378 Marion Cohen Book Review: \booktitleMom the Chemistry Professor: Personal Accounts and Advice from Chemistry Professors Who Are Mothers . . . . . . . . . . . . . . . . 379--383 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 386--386 Maria Deijfen and Alexander E. Holroyd and James B. Martin Friendly Frogs, Stable Marriage, and the Magic of Invariance . . . . . . . . . . 387--402 Juan Monterde and David Rochera Holditch's Ellipse Unveiled . . . . . . 403--421 Frantisek Marko and Semyon Litvinov On the Steiner--Routh Theorem for Simplices . . . . . . . . . . . . . . . 422--435 Marek Balcerzak and Michal Poplawski and Julia Wódka Local Extrema and Nonopenness Points of Continuous Functions . . . . . . . . . . 436--443 Jeremiah Farrell and William Johnston Mathematical Evolution . . . . . . . . . 444--444 Péter E. Frenkel and József Pelikán On the Greatest Common Divisor of the Value of Two Polynomials . . . . . . . . 446--450 Valerio De Angelis The Stern Diatomic Sequence via Generalized Chebyshev Polynomials . . . 451--455 Melvyn B. Nathanson Subalgebras of a Polynomial Ring That Are Not Finitely Generated . . . . . . . 456--458 Beniamin Bogosel A Geometric Proof of the Siebeck--Marden Theorem . . . . . . . . . . . . . . . . 459--463 Haryono Tandra A More Direct Proof of the Extreme Value Theorem . . . . . . . . . . . . . . . . 464--464 Anonymous Problems and Solutions . . . . . . . . . 465--474 Reuben Hersh Book Review: \booktitleElements of Mathematics: From Euclid to Gödel . . . . 475--478 Anonymous Editor's Endnotes . . . . . . . . . . . 480--480 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 481--482 Francis Edward Su Mathematics for Human Flourishing . . . 483--493 Andrey Kupavskii and János Pach From Tarski's Plank Problem to Simultaneous Approximation . . . . . . . 494--505 David Aldous and Weijian Han Introducing Nash Equilibria via an Online Casual Game That People Actually Play . . . . . . . . . . . . . . . . . . 506--517 Grant Cairns Equitable Candy Sharing . . . . . . . . 518--526 Finbarr Holland On the Limiting Behavior of Solutions of Linear Difference Equations . . . . . . 527--534 Paul Carter and David Lowry-Duda On Functions Whose Mean Value Abscissas Are Midpoints, with Connections to Harmonic Functions . . . . . . . . . . . 535--542 Darren B. Glass Klein Four Actions on Graphs and Sets 543--547 Mikhail A. Patrakeev Dissection of an Equilateral Triangle into Five Congruent Open Sets . . . . . 547--547 Heinrich Steinlein Fermat's Little Theorem and Gauss Congruence: Matrix Versions and Cyclic Permutations . . . . . . . . . . . . . . 548--553 Mircea Merca The Riemann Zeta Function With Even Arguments as Sums Over Integer Partitions . . . . . . . . . . . . . . . 554--557 Lee K. Jones An Elementary Derivation of the Numerical Integration Bounds in Beginning Calculus . . . . . . . . . . . 558--561 Romeo Mestrovi\'c A Very Short Proof of the Infinitude of Primes . . . . . . . . . . . . . . . . . 562--562 Anonymous Problems and Solutions . . . . . . . . . 563--571 Jeffrey Nunemacher Book Review: \booktitleVector Calculus, Linear Algebra, and Differential Forms: A Unified Approach (5th Edition) . . . . 572--575 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 577--578 Peter Winkler The Sleeping Beauty Controversy . . . . 579--587 Arseniy Akopyan and Vladislav Vysotsky On the Lengths of Curves Passing Through Boundary Points of a Planar Convex Shape 588--596 Moa Apagodu and Doron Zeilberger Using the ``Freshman's Dream'' to Prove Combinatorial Congruences . . . . . . . 597--608 Philip P. West and Brian D. Sittinger A Further Stroll into the Eisenstein Primes . . . . . . . . . . . . . . . . . 609--620 John C. Bowers and Philip L. Bowers A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space . . . . 621--636 David A. Levin and Yuval Peres Counting Walks and Graph Homomorphisms via Markov Chains and Importance Sampling . . . . . . . . . . . . . . . . 637--641 Anonymous The Other Moore Method . . . . . . . . . 641--641 Christian Axler and Thomas Leßmann On the First $k$-Ramanujan Prime . . . . 642--646 Amrik Singh Nimbran An Infinite Product for the Square Root of an Integer . . . . . . . . . . . . . 647--650 Tomasz Kania On Bases That Are Closed Under Multiplication . . . . . . . . . . . . . 651--653 Óscar Ciaurri Maria Gaetana Agnesi Meets Johannes Kepler . . . . . . . . . . . . . . . . . 654--658 Jitender Singh Another Proof of the Binomial Theorem 658--658 Anonymous Problems and Solutions . . . . . . . . . 659--666 Calvin Jongsma Book Review: \booktitleSourcebook in the Mathematics of Medieval Europe and North Africa . . . . . . . . . . . . . . . . . 667--672 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 673--674 Leonard F. Klosinski and Gerald L. Alexanderson and Mark Krusemeyer The Seventy-Seventh William Lowell Putnam Mathematical Competition . . . . 675--687 Soham Basu and Daniel J. Velleman On Gauss's First Proof of the Fundamental Theorem of Algebra . . . . . 688--694 Bernd C. Kellner and Jonathan Sondow Power-Sum Denominators . . . . . . . . . 695--709 Hugo Parlier and Samuel Zappa Distances in Domino Flip Graphs . . . . 710--722 Stephan Ramon Garcia Linearly Independent Spanning Sets . . . 722--722 Ulrich Abel and Linda Beukemann and Vitaliy Kushnirevych Rolling Curves: An Old Proof of the Roulette Lemma . . . . . . . . . . . . . 723--736 David J. Platt and Timothy S. Trudgian On the Sum of Two Squares and At Most Two Powers of 2 . . . . . . . . . . . . 737--740 Jens Marklof and Andreas Strömbergsson The Three Gap Theorem and the Space of Lattices . . . . . . . . . . . . . . . . 741--745 Zoltán Kánnai A One-to-One Popcorn Function . . . . . 746--748 Stasys Jukna Minkowski Complexity of Sets: An Easy Lower Bound . . . . . . . . . . . . . . 749--753 Anonymous Problems and Solutions . . . . . . . . . 754--762 Anonymous Problems for Metagrobologists: A Collection of Puzzles with Real Mathematical, Logical, or Scientific Content; One Hundred Prisoners and A Light Bulb . . . . . . . . . . . . . . . 763--768 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 769--770 Scott T. Chapman and Joseph A. Gallian From the Guest Editors . . . . . . . . . 771--771 Anonymous About the Cover . . . . . . . . . . . . 772--772 Paul-Jean Cahen and Jean-Luc Chabert and Kiran S. Kedlaya Bhargava's Early Work: The Genesis of $P$-Orderings . . . . . . . . . . . . . 773--790 Colin Adams Turning Knots into Flowers and Related Undergraduate Research . . . . . . . . . 791--806 Cesar E. Silva On Mixing-Like Notions in Infinite Measure . . . . . . . . . . . . . . . . 807--825 Adrian Chun Pong Chu Dihedral Angle of the Regular $n$-Simplex via Menelaus' Theorem . . . 826--826 Yufei Zhao Extremal Regular Graphs: Independent Sets and Graph Homomorphisms . . . . . . 827--843 Rishi Nath Advances in the Theory of Cores and Simultaneous Core Partitions . . . . . . 844--861 Nathan Kaplan Counting Numerical Semigroups . . . . . 862--875 Carlos Castillo-Chavez and Christopher Kribs and Benjamin Morin Student-Driven Research at the Mathematical and Theoretical Biology Institute . . . . . . . . . . . . . . . 876--892 Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . 893--894 Peter Frankl and Amram Meir and János Pach Decomposition of a Cube into Nearly Equal Smaller Cubes . . . . . . . . . . 895--904 Michael Barnsley and Andrew Vince Self-Similar Polygonal Tiling . . . . . 905--921 Emmanuel Tsukerman and Ellen Veomett Brunn--Minkowski Theory and Cauchy's Surface Area Formula . . . . . . . . . . 922--929 Yann Bugeaud and Andrej Dujella and Tomislav Pejkovi\'c and Bruno Salvy Absolute Real Root Separation . . . . . 930--936 Martin Kreh ``Lights Out'' and Variants . . . . . . 937--950 Andrew Granville Squares in Arithmetic Progressions and Infinitely Many Primes . . . . . . . . . 951--954 Joshua Cooper and Anton Swifton Throwing a Ball as Far as Possible, Revisited . . . . . . . . . . . . . . . 955--959 Sunil K. Chebolu and Keir Lockridge How Many Units Can a Commutative Ring Have? . . . . . . . . . . . . . . . . . 960--965 Jen\Ho Szigeti and Leon vanWyk A Constructive Elementary Proof of the Skolem--Noether Theorem for Matrix Algebras . . . . . . . . . . . . . . . . 966--968 Umberto Cerruti and Nadir Murru If the Primes are Finite, Then All of Them Divide the Number One . . . . . . . 969--969 Anonymous Problems and Solutions . . . . . . . . . 970--978 Anonymous Book Review: \booktitleFrom Music to Mathematics: Exploring the Connections, Gareth E. Roberts. Johns Hopkins University Press, Baltimore, MD, 2016. Price: \$49.95 ISBN: 978-1-4214-1918-3} 979--982 Anonymous Editor's Endnotes . . . . . . . . . . . 983--985 Anonymous Monthly Referees For 2017 . . . . . . . 986--988 Anonymous Back Matter . . . . . . . . . . . . . . ??
Adrian Rice Partnership, Partition, and Proof: The Path to the Hardy--Ramanujan Partition Formula . . . . . . . . . . . . . . . . 3--15 Harold P. Boas Cauchy's Residue Sore Thumb . . . . . . 16--28 Anonymous 100 Years Ago This Month in \booktitleThe American Mathematical Monthly, Edited by Vadim Ponomarenko . . 28--28 Kristen Mazur and Mutiara Sondjaja and Matthew Wright and Carolyn Yarnall Approval Voting in Product Societies . . 29--43 David Treeby Further Thoughts on a Paradoxical Tower 44--60 Carl D. Meyer Rank My Update, Please . . . . . . . . . 61--64 Alok Shukla A Short Proof of Cayley's Tree Formula 65--68 John Clifford and Kelly Jabbusch and Michael Lachance Preimages of the Numerical Range . . . . 69--74 Giuseppe De Marco An Almost Everywhere Constant Function Surjective on Every Interval . . . . . . 75--76 Tamás Titkos The Singular Part as Fixed Point . . . . 77--80 Jitender Singh A Noninductive Proof of de Moivre's Formula . . . . . . . . . . . . . . . . 80--80 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 81--89 Geoffrey Dietz The Mathematics Lover's Companion: Masterpieces for Everyone . . . . . . . 90--95
Bruce C. Berndt and Sun Kim and Alexandru Zaharescu The Circle Problem of Gauss and the Divisor Problem of Dirichlet --- Still Unsolved . . . . . . . . . . . . . . . . 99--114 Michael Maltenfort Pascal Functions . . . . . . . . . . . . 115--129 C. Bryan Dawson A New Extension of the Riemann Integral 130--140 Marcin Kulczycki and Dominik Kwietniak and Jian Li Entropy of Subordinate Shift Spaces . . 141--148 Cara D. Brooks and Alberto A. Condori A Resolvent Criterion for Normality . . 149--156 Jonathan Sondow Lorentz Stöer's \booktitleGeometria et Perspectiva . . . . . . . . . . . . . . 157--157 Aaron Melman Optimality of a Polynomial Multiplier 158--163 Rom Pinchasi A Theorem on Unit Segments on the Real Line . . . . . . . . . . . . . . . . . . 164--168 Ralph Howard and Virginia Johnson and George F. McNulty A Functional Equation Characterization of Archimedean Ordered Fields . . . . . 169--172 Christopher Stuart An Inequality Involving $ \sin (n) $ . . 173--174 Wenchang Chu Partial Fractions and Riesz' Interpolation Formula for Trigonometric Polynomials . . . . . . . . . . . . . . 175--178 Anonymous Problems and Solutions . . . . . . . . . 179--187 Robert Cowen Review: \booktitleA Beginner's Guide to Mathematical Logic, By Raymond M. Smullyan. Dover, Mineola, NY, 2014. vi + 284 pp. store.doverpublications.com/0486492370.html ISBN: 978-0-486-49237-7, \$19.95. \booktitle{A Beginner's Further Guide to Mathematical Logic}. By Raymond M. Smullyan. World Scientific, Hackensack, NJ, 2017. x + 278 pp. worldscientific.com/worldscibooks/10.1142/9865 ISBN: 978-981-4725-72-9, \$24.00 (paperback) 188--192
Annalisa Crannell Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2018 to David Bressoud for Distinguished Service to Mathematics . . 195--197 Sam Vandervelde The Worpitzky Numbers Revisited . . . . 198--206 Russell A. Gordon and José Carlos Santos An Interesting Construction Problem . . 207--221 Ángel Plaza The Harmonic Series Diverges . . . . . . 222--222 Gilbert Strang Multiplying and Factoring Matrices . . . 223--230 David Salwinski The Continuous Binomial Coefficient: an Elementary Approach . . . . . . . . . . 231--244 Maxim Gilula A Class of Simple Rearrangements of the Alternating Harmonic Series . . . . . . 245--256 Kevin Woods AdaM and GrahaM Play the Stock Market 257--257 Leo Goldmakher and Paul Pollack Refinements of Lagrange's Four-Square Theorem . . . . . . . . . . . . . . . . 258--263 Peter Shiu A Footnote to the Three Gaps Theorem . . 264--266 Andrew Leahy The Method of Archimedes in the Seventeenth Century . . . . . . . . . . 267--272 Marcin Mazur An Inequality for the Volume of a Tetrahedron . . . . . . . . . . . . . . 273--275 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 276--283 Darren Glass The Joy of SET . . . . . . . . . . . . . 284--288
David Broaddus and Stephen Lovett and Dawson Miller and Caitlin Smith Seeing Curvature on Specular Surfaces 291--305 Larry Carter and Stan Wagon The Mensa Correctional Institute . . . . 306--319 Maria Bras-Amorós A Decoding Approach to Reed--Solomon Codes from Their Definition . . . . . . 320--338 Chungwu Ho and Seth Zimmerman On Certain Dense, Uncountable Subsets of the Real Line . . . . . . . . . . . . . 339--346 Eli Leher is Not 1.41421356237 or Anything of the Sort . . . . . . . . . . . . . . . . . . 346--346 Matthias Keller and Yehuda Pinchover and Felix Pogorzelski An Improved Discrete Hardy Inequality 347--350 Brian Lubeck and Vadim Ponomarenko Subsums of the Harmonic Series . . . . . 351--355 Vaibhav Pandey and Sagar Shrivastava and Balasubramanian Sury A Dedekind Domain with Nontrivial Class Group . . . . . . . . . . . . . . . . . 356--359 Mark B. Villarino The Error in an Alternating Series . . . 360--364 José A. Adell and Alberto Lekuona Binomial Identities and Moments of Random Variables . . . . . . . . . . . . 365--369 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 370--378 Laura Taalman Review: \booktitleVisualizing Mathematics With $3$D Printing by Henry Segerman and Pasta by Design by George Legendre . . . . . . . . . . . . . . . . 379--384
Joe Buhler and Ron Graham and Al Hales Maximally Nontransitive Dice . . . . . . 387--399 Jonathan M. Borwein and Robert M. Corless Gamma and Factorial in the \booktitleMonthly . . . . . . . . . . . 400--424 Abílio Lemos and Pedro H. A. de Oliveira Suggested Corrections for ``A Principal Ideal Domain That Is Not a Euclidean Domain'' . . . . . . . . . . . . . . . . 425--425 Daniel de la Fuente and Rafael Ramírez-Uclés and Juan F. Ruiz-Hidalgo A Visual Model of the Lorentz Triangular Moduli Space . . . . . . . . . . . . . . 426--432 João Lita da Silva On One Type of Generalized Vandermonde Determinants . . . . . . . . . . . . . . 433--442 Chris D. Lynd and James Wright Sharpe Sequences Generated by Powers of the $k$-th-order Fibonacci Recurrence Relation . . . . . . . . . . . . . . . . 443--446 Augustine O. Munagi Set Partitions with Isolated Singletons 447--452 A. G. Smirnov A Gronwall-type Trigonometric Inequality 453--456 Youssef Azouzi Cluster Points of Slow Sequences . . . . 457--461 Eugene Curtin Another Short Proof of the Hairy Ball Theorem . . . . . . . . . . . . . . . . 462--463 Iago Rodríguez-Quintana A Beautiful Continued Fraction for $ \pi $ . . . . . . . . . . . . . . . . . . . 463--463 Anuj Jakhar An Irreducibility Criterion for Polynomials with Integer Coefficients 464--465 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 466--475 Avner Ash Review: \booktitlePrime Numbers and the Riemann Hypothesis by Barry Mazur and William Stein . . . . . . . . . . . . . 476--480
Andrew Granville Using Dynamical Systems to Construct Infinitely Many Primes . . . . . . . . . 483--496 Ying Chai and Liping Yuan and Tudor Zamfirescu Rupert Property of Archimedean Solids 497--504 Greg Huber and Kay Pechenick Shultz and John E. Wetzel The $n$-Cube is Rupert . . . . . . . . . 505--512 Mark B. Villarino and William Gasarch and Kenneth W. Regan Hilbert's Proof of His Irreducibility Theorem . . . . . . . . . . . . . . . . 513--530 Philip de Castro and Desiree Domini and Tom Edgar and Devon M. Johnson and Steven Klee and Ranjani Sundaresan Counting Binomial Coefficients Divisible by a Prime Power . . . . . . . . . . . . 531--540 Peter McGrath A Note Regarding Hopf's Umlaufsatz . . . 541--544 Angelina Y. M. Chin Finite Rings of Odd Order with Few Nilpotent and Idempotent Elements . . . 545--548 Shamil Asgarli A New Proof of Warning's Second Theorem 549--553 Jitender Singh A Short Proof That Lebesgue Outer Measure of an Interval Is Its Length . . 553--553 Yves Coud\`ene A Strange Inequality Concerning Alternating Series . . . . . . . . . . . 554--557 Kapil R. Shenvi Pause Basel Problem: a Solution Motivated by the Power of a Point . . . . . . . . . . 558--560 Samuel G. Moreno and Esther M. García-Caballero A Characterization of Bernoulli Differential Equations . . . . . . . . . 561--561 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 562--570 Jason Rosenhouse Reviews . . . . . . . . . . . . . . . . 571--576
Ian Morrison Sacks of Dice with Fair Totals . . . . . 579--592 Edray H. Goins and Pamela E. Harris and Bethany Kubik and Aba Mbirika Lattice Point Visibility on Generalized Lines of Sight . . . . . . . . . . . . . 593--601 Andrew Gard The Wild Goose Chase Problem . . . . . . 602--611 Ghada Al-Afifi and Mowaffaq Hajja and Ahmad Hamdan Another $n$-Dimensional Generalization of Pompeiu's Theorem . . . . . . . . . . 612--622 Melvyn B. Nathanson An Elementary Proof for the Krull Dimension of a Polynomial Ring . . . . . 623--637 Allan Berele and Stefan Catoiu Nonuniqueness of Sixpartite Points . . . 638--642 Scott T. Chapman What Happens When the Division Algorithm ``Almost'' Works . . . . . . . . . . . . 643--647 George Stoica When Must a Flat Function be Identically 0? . . . . . . . . . . . . . . . . . . . 648--649 Marian Gencev On a Proof of the Inequality Between the Arithmetic and Geometric Means . . . . . 650--652 Daniel L. Reinholz Peer Feedback for Learning Mathematics 653--658 Enrique Treviño A short proof of a sum of powers formula 659--659 Gerald A. Edgar and Daniel Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 660--668 Alex Meadows Reviews . . . . . . . . . . . . . . . . 669--672
Mark Krusemeyer and Daniel H. Ullman The Seventy-Eighth William Lowell Putnam Mathematical Competition . . . . . . . . 675--688 Stephanie Chan Rational Right Triangles of a Given Area 689--703 John Pearson Vi\`ete's Formula, Knar's Formula, and the Geometry of the Gamma Function . . . 704--714 Erik Talvila You Know You're a Mathematician If \ldots . . . . . . . . . . . . . . . . . 714--714 Alejandro H. Morales and Igor Pak and Greta Panova Why Is Pi Less Than Twice Phi? . . . . . 715--723 J. J. P. Veerman Social Balance and the Bernoulli Equation . . . . . . . . . . . . . . . . 724--732 Naoki Shioji Simple Proofs of the Uniform Convexity of $ L^p $ and the Riesz Representation Theorem for $ L^p $ . . . . . . . . . . 733--738 Krzysztof Chris Ciesielski Monsters in Calculus . . . . . . . . . . 739--744 Aalok Thakkar Infinitude of Primes Using Formal Languages . . . . . . . . . . . . . . . 745--749 T. N. L. Patterson Sines, Cosines, Square Roots, and Binary Bits . . . . . . . . . . . . . . . . . . 750--754 Mark Stander The Smallest Solution to $ A B = C $, Where $A$, $B$, and $C$ are Square Matrices Composed of Distinct Primes . . 754--754 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 755--763 Russell Merris Reviews . . . . . . . . . . . . . . . . 764--768
Steven J. Brams and Mehmet S. Ismail and D. Marc Kilgour and Walter Stromquist Catch-Up: a Rule That Makes Service Sports More Competitive . . . . . . . . 771--796 Kenneth S. Williams Everything You Wanted To Know About $ a x^2 + b y^2 + c z^2 + d t^2 $ But Were Afraid To Ask . . . . . . . . . . . . . 797--810 Titu Andreescu and Oleg Mushkarov Quadratic Forms, Chebyshev Polynomials, and Geometric Inequalities . . . . . . . 811--819 Matthew C. H. Tointon The Mahler Conjecture in Two Dimensions via the Probabilistic Method . . . . . . 820--828 Lee Sallows A Self-Descriptive Crossword Puzzle . . 829--829 Yuliy Baryshnikov and Robert Ghrist Stokes's Theorem, Data, and the Polar Ice Caps . . . . . . . . . . . . . . . . 830--834 Davit Harutyunyan When the Cauchy Inequality Becomes a Formula . . . . . . . . . . . . . . . . 835--838 Pedro Ribeiro Another Proof of the Famous Formula for the Zeta Function at Positive Even Integers . . . . . . . . . . . . . . . . 839--841 Paolo Leonetti A Characterization of Convex Functions 842--844 Joseph Plante Cubic Equations from an Analytic Point of View . . . . . . . . . . . . . . . . 845--849 Bryan Park On the Divergence of the Prime Harmonic Series . . . . . . . . . . . . . . . . . 850--850 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 851--859 Marion Cohen Reviews . . . . . . . . . . . . . . . . 860--864 Lee Sallows Solution to the Self-Descriptive Crossword Puzzle . . . . . . . . . . . . 864--864
Noah Giansiracusa and Cameron Ricciardi Geometry in the Courtroom . . . . . . . 867--877 Boris Alexeev and Dustin G. Mixon An Impossibility Theorem for Gerrymandering . . . . . . . . . . . . . 878--884 Pisheng Ding On the Lengths of Level Curves . . . . . 885--900 Achim Clausing Ducci Matrices . . . . . . . . . . . . . 901--921 Chen Zheng and Zhijun Zhou A Generalization of a \booktitleMonthly Problem . . . . . . . . . . . . . . . . 922--922 J. A. Hocutt and P. L. Robinson Everywhere Differentiable, Nowhere Continuous Functions . . . . . . . . . . 923--928 Mircea Merca and Maxie D. Schmidt A Partition Identity Related to Stanley's Theorem . . . . . . . . . . . 929--933 Lior Bary-Soroker and Ofir Gorodetsky Roots of Polynomials and the Derangement Problem . . . . . . . . . . . . . . . . 934--938 José Antonio Torné and Juan Luis Varona The Lindemann Theorem for Matrices . . . 939--940 Peng Liu and Shibo Liu On the Surjectivity of Smooth Maps into Euclidean Spaces and the Fundamental Theorem of Algebra . . . . . . . . . . . 941--943 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 944--952 Robert M. Guralnick and Gary M. Seitz Reviews . . . . . . . . . . . . . . . . 953--955 Susan Jane Colley Editor Editor's Endnotes . . . . . . . . . . . 956--957 Anonymous \booktitleMonthly Referees for 2018 . . 958--960
Susan Jane Colley Letter from the Editor . . . . . . . . . 3--3 Jayadev S. Athreya and Bruce Reznick and Jeremy T. Tyson Cantor Set Arithmetic . . . . . . . . . 4--17 Florian Frick and Kelsey Houston-Edwards and Frédéric Meunier Achieving Rental Harmony with a Secretive Roommate . . . . . . . . . . . 18--32 Javier Sánchez-Reyes The Joukowsky Map Reveals the Cubic Equation . . . . . . . . . . . . . . . . 33--40 Daniel P. Bossaller and Sergio R. López-Permouth On the Associativity of Infinite Matrix Multiplication . . . . . . . . . . . . . 41--52 Waldemar Pompe Concurrent Lines in the Napoleon-style Configurations . . . . . . . . . . . . . 53--59 Benjamin Sambale Pseudo Sylow Numbers . . . . . . . . . . 60--65 William Cocke and Geetha Venkataraman On the Number of Elements of Maximal Order in a Group . . . . . . . . . . . . 66--69 Dylan Fridman and Juli Garbulsky and Bruno Glecer and James Grime and Massi Tron Florentin A Prime-Representing Constant . . . . . 70--73 José Manuel Rodríguez Caballero A Characterization of the Hypotenuses of Primitive Pythagorean Triangles Using Partitions into Consecutive Parts . . . 74--77 Vadim Ponomarenko Help with the Jumble . . . . . . . . . . 77--77 John Donnelly On a Conjecture of Fickett . . . . . . . 78--80 K. Kuhapatanakul and K. Thongsing Generalizations of the Fibonacci--Lucas Relations . . . . . . . . . . . . . . . 81--81 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 82--90 Tullia Dymarz Reviewed by Reviews . . . . . . . . . . . . . . . . 91--96
Pamela Gorkin Four Theorems with Their Foci on Ellipses . . . . . . . . . . . . . . . . 99--111 Arpan Sadhukhan A Simple Construction to Prove Mycielski's Theorem . . . . . . . . . . 112--112 Jason Cantarella and Tom Needham and Clayton Shonkwiler and Gavin Stewart Random Triangles and Polygons in the Plane . . . . . . . . . . . . . . . . . 113--134 Mowaffaq Hajja and Jonathan Sondow Newton Quadrilaterals, the Associated Cubic Equations, and Their Rational Solutions . . . . . . . . . . . . . . . 135--150 J. Jerónimo-Castro and C. Yee-Romero Characterizations of the Euclidean Ball by Intersections with Planes and Slabs 151--157 Maxim Arnold and Anatoly Eydelzon On Matrix Pythagorean Triples . . . . . 158--160 Jayadev S. Athreya and David Aulicino A Trajectory from a Vertex to Itself on the Dodecahedron . . . . . . . . . . . . 161--162 Paolo Leonetti Convergence Rates of Subseries . . . . . 163--167 B. Sury A Ring-theoretic Approach to Bound the Totient Function . . . . . . . . . . . . 167--167 Nicholas Phat Nguyen A Note on Cyclotomic Integers . . . . . 168--172 Dorin Andrica and Vlad Crisan The Smallest Nontrivial Solution to $ x_k \equiv 1 (\bmod n) $ and Related Sequences . . . . . . . . . . . . . . . 173--178 Robert G. Donnelly and Molly W. Dunkum The Group Action Tri-cycle Theorem . . . 179--179 Edited by Gerald A. Edgar and Daniel H. Ullman and Douglas B. West and with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 180--188 Reviewed by Bruce Berndt Reviews . . . . . . . . . . . . . . . . 189--192
Joanne Peeples and James Álvarez and Ruth Charney and John Harris and Jim Lewis and Nancy Neudauer Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2019 to Philip Uri Treisman for Distinguished Service to Mathematics 195--198 Daniel H. Ullman and Daniel J. Velleman Differences of Bijections . . . . . . . 199--216 J.-P. Allouche Two Binomial Identities of Ruehr Revisited . . . . . . . . . . . . . . . 217--225 K. Soundararajan Equidistribution of Zeros of Polynomials 226--236 Oscar M. Perdomo The Round Taylor Method . . . . . . . . 237--251 V. P. Ramesh and R. Thangadurai and R. Thatchaayini A Note on Gauss's Theorem on Primitive Roots . . . . . . . . . . . . . . . . . 252--254 Shirley Llamado Yap A Theodorus Construction . . . . . . . . 255--259 Jean Mawhin Simple Proofs of the Hadamard and Poincaré--Miranda Theorems Using the Brouwer Fixed Point Theorem . . . . . . 260--263 Neil Falkner Hahn's Proof of the Hahn Decomposition Theorem, and Related Matters . . . . . . 264--268 Tamás Forgács and Jack Luong and Joshua Williamson A Note on Infinite Series with Recursively Defined Terms . . . . . . . 269--274 Bill Rounds Euclid's Lemma and the Square Root of 2 274--274 Russell A. Gordon Comments on ``Subsums of the Harmonic Series'' . . . . . . . . . . . . . . . . 275--279 Edited by Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 280--288
Deborah E. Seacrest and Tyler Seacrest The Prisoner Shouting Puzzle and Variations . . . . . . . . . . . . . . . 291--305 Alan D. Taylor and Stan Wagon A Paradox Arising from the Elimination of a Paradox . . . . . . . . . . . . . . 306--318 Finbarr Holland and Roger Smyth Cardioids and Self-inversive Cubic Polynomials . . . . . . . . . . . . . . 319--329 Scott T. Chapman So What Is Class Number 2? . . . . . . . 330--339 M. G. Mahmoudi A Geometric Interpretation of the Simplicity of $ {\rm SO}(3) $ . . . . . 340--350 Simon Demers The Smallest Number That Cannot Be Collapsed Using Fewer Than 6 Plus Signs is 3003344034004 . . . . . . . . . . . . 351--351 Makoto Ozawa and Scott A. Taylor Two More Proofs that the Kinoshita Graph is Knotted . . . . . . . . . . . . . . . 352--357 Péter Kórus Notes on Projectile Motion . . . . . . . 358--360 M. L. Glasser A Note on Beukers's and Related Double Integrals . . . . . . . . . . . . . . . 361--363 Stasys Jukna Coin Flipping Cannot Shorten Arithmetic Computations . . . . . . . . . . . . . . 364--366 Stephan Berendonk A Napoleonic Theorem for Trapezoids . . 367--369 Edited by Gerald A. Edgar and Daniel H. Ullman and Douglas B. West and with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 370--378 Lowell Beineke Reviews . . . . . . . . . . . . . . . . 379--384
Bruce Torrence Passing the Buck and Firing Fibonacci: Adventures with the Stochastic Abacus 387--399 Dmitri V. Fomin Is the Multiset of $n$ Integers Uniquely Determined by the Multiset of Its $s$-sums? . . . . . . . . . . . . . . . 400--417 Tim Antonelli A Surprising Link Between Integer Partitions and Euler's Number $e$ . . . 418--429 Niels Juul Munch A Chebyshev Theorem for Ellipses in the Complex Plane . . . . . . . . . . . . . 430--436 Anonymous The Hardest Jumbles . . . . . . . . . . 436--436 Thomas R. Cameron The Determinant from Signed Volume to the Laplace Expansion . . . . . . . . . 437--447 Olivier Schneegans How Close to 10 Is $ \pi^2 $ ? . . . . . 448--448 Gerd Herzog and Peer Chr. Kunstmann Korovkin's Theorem for Functionals and Limits for Box Integrals . . . . . . . . 449--454 Edited by Vadim Ponomarenko 100 Years Ago This Month in \booktitleThe American Mathematical Monthly . . . . . . . . . . . . . . . . 454--454 R. R. Andruszkiewicz and K. Pryszczepko A Curious Characterization of Subrings of the Field $ \mathbb {Q} $ and Applications . . . . . . . . . . . . . . 455--458 Raymond Mortini A Simpler Proof of Cohen's Factorization Theorem . . . . . . . . . . . . . . . . 459--463 Aleksander B\laszczyk A Simple Proof of Sierpi\'nski's Theorem 464--466 Angel Plaza $k$-th Power of a Partial Sum . . . . . 467--467 Edited by Gerald A. Edgar and Daniel H. Ullman and Douglas B. West and with the collaboration of Paul Bracken Problems and Solutions . . . . . . . . . 468--476 Reviewed by Thomas Ratliff Reviews . . . . . . . . . . . . . . . . 477--479 Anonymous Solution to the Hardest Jumbles . . . . 479--479 Susan Jane Colley Editor's Endnotes . . . . . . . . . . . 480--480
Colin Adams and Allison Henrich and Kate Kearney and Nicholas Scoville Knots Related by Knotoids . . . . . . . 483--490 Ronaldo Garcia Elliptic Billiards and Ellipses Associated to the 3-Periodic Orbits . . 491--504 Tiffany Kolba and Anthony Coniglio and Sarah Sparks and Daniel Weithers Noise-Induced Stabilization of Perturbed Hamiltonian Systems . . . . . . . . . . 505--518 José Hernández Santiago The Group-Theoretic Analog of Kuratowski's Closure-Complement Theorem 519--526 Jennifer Brooks An Interesting Family of Symmetric Polynomials . . . . . . . . . . . . . . 527--540 Judy Holdener and Emily Rachfal Perfect and Deficient Perfect Numbers 541--546 David Treeby Relativity . . . . . . . . . . . . . . . 546--546 K. C. Ciesielski and M. E. Martínez-Gómez and J. B. Seoane-Sepúlveda ``Big'' Continuous Restrictions of Arbitrary Functions . . . . . . . . . . 547--552 Jonathan M. Fraser Almost Arithmetic Progressions in the Primes and Other Large Sets . . . . . . 553--558 Hunter Swan Nonnegative Eigenvectors of Symmetric Matrices . . . . . . . . . . . . . . . . 559--560 Jacques Gélinas and Alexander G. Smirnov Integral Representation for Derivatives of $ \cos (x) $ . . . . . . . . . . . . 561--561 Edited by Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 562--570 Dominic Lanphier Reviews . . . . . . . . . . . . . . . . 571--576
John B. Little The Many Lives of the Twisted Cubic . . 579--592 Kristopher Tapp Measuring Political Gerrymandering . . . 593--609 Athanase Papadopoulos Three Theorems of Menelaus . . . . . . . 610--619 Anonymous The Paul R. Halmos-Lester R. Ford Awards for 2018 . . . . . . . . . . . . . . . . 619--619 Anatolii Grinshpan and Hugo J. Woerdeman A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem . . . . . . . . 620--627 Michael Maltenfort Decimal Selection Functions . . . . . . 628--634 Malik Younsi Peano Curves in Complex Analysis . . . . 635--640 Graham Jameson and Peter R. Mercer The Logarithmic Mean Revisited . . . . . 641--645 Marc Chamberland and Eugene A. Herman Arctangent Formulas and Pi . . . . . . . 646--650 Ioulia N. Baoulina Integer Ratios of Consecutive Alternating Power Sums . . . . . . . . . 651--654 Yossi Lonke Shadows of Cube Vertices . . . . . . . . 655--656 Christian Aebi 53 Is the Smallest Prime That Is Not the Sum or Difference of Powers of the First Two Prime Numbers . . . . . . . . . . . 657--657 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 658--666 Karl-Dieter Crisman Reviews . . . . . . . . . . . . . . . . 667--672
Mark Krusemeyer and Daniel H. Ullman The Seventy-Ninth William Lowell Putnam Mathematical Competition . . . . . . . . 675--687 Carl Pomerance and Chris Spicer Proof of the Sheldon Conjecture . . . . 688--698 Niels Lauritzen and Jesper Funch Thomsen A Euclidean Algorithm for Integer Matrices . . . . . . . . . . . . . . . . 699--699 Rainer Hegselmann and Ulrich Krause Consensus and Fragmentation of Opinions with a Focus on Bounded Confidence . . . 700--716 Erik Talvila Fourier Transform Inversion Using an Elementary Differential Equation and a Contour Integral . . . . . . . . . . . . 717--727 Florian Luca and Pantelimon Stanica Perfect Squares as Concatenation of Consecutive Integers . . . . . . . . . . 728--734 James East and Ron Niles Integer Triangles of Given Perimeter: a New Approach via Group Theory . . . . . 735--739 Harold W. Ellingsen Jr. A Fresh Look at Highly Composite Numbers 740--741 Fiachra Knox and Bojan Mohar and David R. Wood A Golden Ratio Inequality for Vertex Degrees of Graphs . . . . . . . . . . . 742--747 Misha Kutzman and Vadim Ponomarenko Count to Six in Six Languages . . . . . 747--747 Ashish Goyal and Hemant Kalra and Deepak Gumber On the Probability That an Automorphism Fixes a Group Element . . . . . . . . . 748--753 André Pierro de Camargo A Straightforward Approach to the Product Rule . . . . . . . . . . . . . . 754--754 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 755--763 Priscilla Bremser Reviews . . . . . . . . . . . . . . . . 764--768
Lionel Ponton The Calkin--Wilf Tree of a Quadratic Surd . . . . . . . . . . . . . . . . . . 771--785 Rick Mabry Fibonacci Numbers, Integer Compositions, and Nets of Antiprisms . . . . . . . . . 786--801 Peter Shiu On Erd\Hos's Last Equation . . . . . . . 802--808 G. J. O. Jameson Operator-valued Extensions of Matrix-norm Inequalities . . . . . . . . 809--815 Fredrik Ekström Dimension of Random Limsup Sets . . . . 816--824 Seth Zimmerman and Chungwu Ho Partitioning the Real Line into an Uncountable Collection of Everywhere Uncountably Dense Sets . . . . . . . . . 825--834 Antonín Slavík Unbiased Version of Hall's Marriage Theorem in Matrix Form . . . . . . . . . 835--837 Manor Mendel A Simple Proof of the Johnson--Lindenstrauss Extension Theorem 838--840 Enrique Treviño Probabilistic Proof that $ 1 + 2 + \cdots + n = n (n + 1) / 2 $ . . . . . . 840--840 Franz Embacher and Hans Humenberger A Note on the Stammler Hyperbola . . . . 841--844 Iris Gaber and Arieh Lev and Romina Zigdon Insights and Observations on Teaching the Intermediate Value Theorem . . . . . 845--849 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 850--858 Benjamin Braun and Santiago de León and Kyle Franz and Sami Sultan Base-$b$ Representations . . . . . . . . 859--859 Nicholas Scoville Reviews . . . . . . . . . . . . . . . . 860--864
Norbert Henze and Günter Last Absent-Minded Passengers . . . . . . . . 867--875 Vitaly Bergelson and Joseph Vandehey A Hot Spot Proof of the Generalized Wall Theorem . . . . . . . . . . . . . . . . 876--890 Hugues Bellemare and Yves Langlois and Thomas Ransford A Positivity Conjecture Related to the Riemann Zeta Function . . . . . . . . . 891--904 Balázs Gerencsér and Viktor Harangi Too Acute to Be True: The Story of Acute Sets . . . . . . . . . . . . . . . . . . 905--914 Mark Huber Halving the Bounds for the Markov, Chebyshev, and Chernoff Inequalities Using Smoothing . . . . . . . . . . . . 915--927 Bogdan Veklych A Minimalist Proof of the Law of Quadratic Reciprocity . . . . . . . . . 928--928 Gérard Lavau The Truncated Tetrahedron Is Rupert . . 929--932 Meinolf Geck Eigenvalues and Polynomial Equations . . 933--935 Bernardo de la Calle Ysern Asymptotically Stable Equilibria of Gradient Systems . . . . . . . . . . . . 936--939 B. Sury Lower Bound for the Least Common Multiple . . . . . . . . . . . . . . . . 940--942 François Huppé and Vadim Ponomarenko Primes in $ (0, n] $ vs. $ (n, m] $ . . 942--942 Anuj Jakhar A Useful Irreducibility Result for Integer Polynomials . . . . . . . . . . 943--944 Hongwei Lou Remark on ``When Must a Flat Function be Identically 0?'' . . . . . . . . . . . . 945--945 Gerald A. Edgar and Daniel H. Ullman and Douglas B. West Problems and Solutions . . . . . . . . . 946--954 Dylan A. King and Thomas C. Martinez and Steven J. Miller and Chenyang Sun Reviews . . . . . . . . . . . . . . . . 955--958 Marion Deutsche Cohen End . . . . . . . . . . . . . . . . . . 958--958 Susan Jane Colley Editor's Endnotes . . . . . . . . . . . 959--960 Anonymous \booktitleMonthly Referees for 2019 . . i--iv