The American Mathematical Monthly, Volume 123

Volume 123, Number 1, 2016

Original Articles

• 
  Richard D. Neidinger:
  A Fair-Bold Gambling Function Is Simply Singular. 3-18
• 
  Adrien Kassel, David B. Wilson:
  The Looping Rate and Sandpile Density of Planar Graphs. 19-39
• 
  José Ángel Cid, 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, Chester Weatherby:
  A Generalization of Euler's Theorem for ζ(2k). 53-65
• 
  Shivarajkumar:
  Beyond Schur's Conjecture. 66-70
• 
  Yaroslav Shitov:
  The Diameter of Chess Grows Exponentially. 71-76
• 
  Daniel J. Velleman:
  Monthly Gems. 77

Notes

• 
  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
• 
  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

Original Articles

• 
  Problems And Solutions. 97-105

Reviews

• 
  Jeffrey Nunemacher, Darren B. Glass:
  Reviews. 106-111

Original Articles

• 
  József Sándor:
  A Note on the Logarithmic Mean. 112

Volume 123, Number 2, 2016

Original Articles

• 
  Francis C. Motta, Patrick D. Shipman, Bethany Springer:
  Optimally Topologically Transitive Orbits in Discrete Dynamical Systems. 115-135
• 
  Ian Morrison, David Swinarski:
  Can You Play a Fair Game of Craps with a Loaded Pair of Dice? 136-148
• 
  Deborah A. Kent, David J. Muraki:
  A Geometric Solution of a Cubic by Omar Khayyam... 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
• 
  Josh Hiller:
  Old Friends in Unexpected Places: Pascal (and Other) Matrices in GLn(ℂ). 161-167
• 
  Richard Blecksmith, John Brillhart, Michael Decaro:
  Using Conic Sections to Factor Integers. 168-174

Notes

• 
  Michael Z. Spivey:
  Probabilistic Proofs of a Binomial Identity, Its Inverse, and Generalizations. 175-180
• 
  E. W. Dekking, F. Michel 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

Original Articles

• 
  Problems and Solutions. 197-204

Reviews

• 
  Jeffrey Nunemacher:
  Reviews. 205-208

Volume 123, Number 3, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  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, Oleg A. Ivanov, Alexander S. Merkurjev:
  Milnor's Lemma, Newton's Method, and Continued Fractions. 258-266
• 
  Clark Kimberling, Kenneth B. Stolarsky:
  Slow Beatty Sequences, Devious Convergence, and Partitional Divergence. 267-273

Notes

• 
  Steve Butler, Ron Graham, Richard Stong:
  Inserting Plus Signs and Adding. 274-279
• 
  Tom Mertens, Jeff Weeks:
  Electromagnetism in a Multiconnected Universe. 280-286
• 
  Jeffrey S. Ovall:
  The Laplacian and Mean and Extreme Values. 287-291
• 
  Peter J. McGrath:
  On the Smooth Jordan Brouwer Separation Theorem. 292-295
• 
  José Luis Ramírez:
  An Identity of Carlitz and Its Generalization. 295

Original Articles

• 
  Problems and Solutions. 296-303

Reviews

• 
  Jeffrey Nunemacher, Craig H. Jackson:
  Reviews. 304-308

Volume 123, Number 4, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Paul-Jean Cahen, Jean-Luc Chabert:
  What You Should Know About Integer-Valued Polynomials. 311-337
• 
  Keith Johnson, Kira Scheibelhut:
  Rational Polynomials That Take Integer Values at the Fibonacci Numbers. 338-346
• 
  Gary Brookfield:
  Factoring Forms. 347-362
• 
  Grant Cairns, Yuri Nikolayevsky, Gavin Rossiter:
  Conewise Linear Periodic Maps of the Plane with Integer Coefficients. 363-375
• 
  Mohamed Ayad, Omar Kihel, Jesse Larone:
  When Does a Given Polynomial with Integer Coefficients Divide Another? 376-381

Notes

• 
  Neil J. Calkin, Beth Novick, 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
• 
  Ovidiu Costin, Neil Falkner, Jeffery D. McNeal:
  Some Generalizations of the Riemann-Lebesgue Lemma. 387-391
• 
  Peter S. Landweber, Emanuel A. Lazar, Neel Patel:
  On Fiber Diameters of Continuous Maps. 392-397
• 
  Daniel López-Aguayo:
  Irrationality via Maximality. 397

Original Articles

• 
  Dennis S. Bernstein, Khaled F. Aljanaideh, Arthur E. Frazho:
  Laurent Series and ℓp Sequences. 398
• 
  Problems and Solutions. 399-406

Reviews

• 
  Jeffrey Nunemacher, Thomas Garrity:
  Reviews. 407-412

Volume 123, Number 5, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Søren Eilers:
  The LEGO Counting Problem. 415-426
• 
  Harold P. Boas:
  Mocposite Functions. 427-438
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  A New Look at Surfaces of Constant Curvature. 439-447
• 
  Jaime Cruz-Sampedro, 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
• 
  Gary L. Mullen, Daniel Panario, David Thomson:
  Fast and Simple Modular Interpolation Using Factorial Representation. 471-480
• 
  Iosif Pinelis:
  On Measurable Semigroups in ℝ. 481

Notes

• 
  Arseniy Sheydvasser:
  A Corrigendum to Unreasonable Slightness. 482-485
• 
  Karl Dilcher, Christophe Vignat:
  Euler and the Strong Law of Small Numbers. 486-490
• 
  Tim Hsu:
  Rational Nonaxis Points on the Unit Circle Have Irrational Angles. 490
• 
  Iosif Pinelis:
  Explicit Additive Decomposition of Norms on ℝ2. 491-496
• 
  Michael Gaul, Fred Kuczmarski:
  Parabolas and Archimedes' 2/3-Property. 497-501
• 
  Peter J. McGrath:
  An Extremely Short Proof of the Hairy Ball Theorem. 502-503

Original Articles

• 
  Problems and Solutions. 504-511

Reviews

• 
  Jeffrey Nunemacher, Gerald L. Alexanderson:
  Reviews. 512-514

Miscellany

• 
  Scott T. Chapman:
  Editor's End Notes. 515-516

Volume 123, Number 6, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Jennifer M. Johnson, János Kollár:
  Arcology. 519-541
• 
  Steve Butler, Persi Diaconis, Ron Graham:
  The Mathematics of the Flip and Horseshoe Shuffles. 542-556
• 
  Valerio De Angelis, 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

Notes

• 
  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
• 
  Pham Duy Khanh, Marc Lassonde:
  Quasiconvex Linear Perturbations and Convexity. 605-608
• 
  Ariel Amir, Mikhail Lemeshko, Tadashi Tokieda:
  Surprises in Numerical Expressions of Physical Constants. 609-612

Original Articles

• 
  Problems and Solutions. 613-620

Reviews

• 
  Jeffrey Nunemacher, Leslie Hogben, Mark Hunacek:
  Reviews. 621-624

Volume 123, Number 7, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Laura Florescu, Lionel Levine, Yuval Peres:
  The Range of a Rotor Walk. 627-642
• 
  Lawrence Zalcman:
  A Tale of Three Theorems. 643-656
• 
  Márton Balázs, Áron Folly:
  An Electric Network for Nonreversible Markov Chains. 657-682
• 
  Vincent E. Coll, Jeff Dodd:
  A Characteristic Averaging Property of the Catenary. 683-688
• 
  Dennis Ivanov, Serge Tabachnikov:
  The Six Circles Theorem Revisited. 689-698

Notes

• 
  Arnon Avron, 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 ζ(2m) by Using Telescoping Sums. 710-715
• 
  Yuanyuan Yao, Wenxia Li:
  Generating Iterated Function Systems for the Vicsek Snowflake and the Koch Curve. 716-721

Original Articles

• 
  Problems and Solutions. 722-730

Reviews

• 
  Jeffrey Nunemacher, Matthew Richey:
  Reviews. 731-736

Volume 123, Number 8, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Leonard F. Klosinski, Gerald L. Alexanderson, Mark Krusemeyer:
  The Seventy-Sixth William Lowell Putnam Mathematical Competition. 739-752
• 
  Jeffrey C. Lagarias:
  Erdős, Klarner, and the 3x + 1 Problem. 753-776
• 
  Dvij Bajpai, Daniel J. Velleman:
  Anonymity in Predicting the Future. 777-788
• 
  Philippe Caldero, Jérôme Germoni:
  Equilateral Triangles and the Fano Plane. 789-801
• 
  T. S. Michael, Val Pinciu:
  The Art Gallery Theorem, Revisited. 802-807
• 
  Lon H. Mitchell, Michael A. Jones, Brittany Shelton:
  Abelian and Non-Abelian Triangle Mysteries. 808-813

Notes

• 
  Yong Kong, Shaowei Zhang:
  The Adventitious Angles Problem: The Lonely Fractional Derived Angle. 814-816
• 
  Jesús Jerónimo-Castro, Carlos Yee-Romero:
  Maximal Isoptic Chords of Convex Curves. 817-820
• 
  Olivier de La Grandville:
  An Alternate Derivation of the Euler-Poisson Equation. 821-824
• 
  Jan A. Grzesik:
  Yet Another Analytic Proof of Napoleon's Theorem. 824
• 
  Bálint Farkas, Sven-Ake Wegner:
  Variations on Barbălat's Lemma. 825-830

Original Articles

• 
  Problems and Solutions. 831-839

Reviews

• 
  Jeffrey Nunemacher, Mark Kidwell:
  Reviews. 840-843
• 
  Halil Mutuk:
  A Physical Proof for Cauchy's Inequality. 843

Volume 123, Number 9, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Scott T. Chapman:
  A Letter From the Editor: Jonathan M. Borwein (1951-2016). 847-848
• 
  Paul Baginski, Ryan Rodriguez, George J. Schaeffer, 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
• 
  Joshua Brown Kramer, Jonathan Cutler, A. J. Radcliffe:
  The Multistep Friendship Paradox. 900-908
• 
  Sean Eastman, Selwyn Hollis, Kawee Numpacharoen, Jared Schlieper:
  The Volume of the Spatial Region Corresponding to n × n Correlation Matrices. 909-918
• 
  Ivica Martinjak:
  Two Extensions of the Sury's Identity. 919

Notes

• 
  Bernd Schomburg:
  Primitivity and Orbit Decomposition. 920-923
• 
  Adrian W. Dudek:
  On the Success of Mishandling Euclid's Lemma. 924-927
• 
  Alan J. Hoffman, 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

Original Articles

• 
  Problems and Solutions. 941-948

Reviews

• 
  Jeffrey Nunemacher, Gerald B. Folland:
  Reviews. 949-952

Volume 123, Number 10, 2016

Miscellany

• 
  Editorial Board.

Original Articles

• 
  Scott T. Chapman:
  A Letter from the Editor: The Long and Winding Road. 955-958
• 
  Single Digit NFL Scores. 959
• 
  Alfred Geroldinger:
  Sets of Lengths. 960-988
• 
  Anton A. Klyachko, Anton N. Vassilyev:
  Balanced Factorizations. 989-1000
• 
  Melvyn B. Nathanson:
  Cantor Polynomials and the Fueter-Pólya Theorem. 1001-1012
• 
  Aaron M. Broussard, Martin E. Malandro, Abagayle Serreyn:
  Optimizing the Video Game Multi-Jump: Player Strategy, AI, and Level Design. 1013-1032

Notes

• 
  Jeffrey C. Lagarias, Takumi Murayama, David Harry Richman:
  Dilated Floor Functions That Commute. 1033-1038
• 
  Stephan Ramon Garcia, Florian Luca:
  Quotients of Fibonacci Numbers. 1039-1044
• 
  Richard Ehrenborg, Alex Happ:
  Parking Cars of Different Sizes. 1045-1048
• 
  Corrigendum to "A New Proof of the Change of Variable Theorem for the Riemann Integral". 1049

Original Articles

• 
  Problems and Solutions. 1050-1057

Reviews

• 
  Jeffrey Nunemacher, Chris A. Marx:
  Reviews. 1058-1061

Miscellany

• 
  Monthly Referees for 2016. 1062-1066