The American Mathematical Monthly, Volume 111

Volume 111, Number 1, January 2004

• 
  Ivor Grattan-Guinness:
  History or Heritage? An Important Distinction in Mathematics and for Mathematics Education. 1-12
• 
  Michael A. Bennett, Bruce Reznick:
  Positive Rational Solutions to x^y = y^mx: A Number-Theoretic Excursion. 13-21
• 
  Richard Jerrard, John E. Wetzel:
  Prince Rupert's Rectangles. 22-31
• 
  Steven G. Krantz, Jeffery D. McNeal:
  Creating More Convergent Series. 32-38
• 
  Burkard Polster:
  Variations on a Theme in Paper Folding. 39-47

Notes

• 
  Sey Y. Kim:
  An Elementary Proof of the Quadratic Reciprocity Law. 48-50
• 
  Götz Trenkler:
  Matrices Which Take a Given Vector into a Given Vector: Revisited. 50-52
• 
  Thomas J. Osler:
  Finding ζ(2p) from a Product of Sines. 52-54
• 
  S. H. Kulkarni:
  A Very Simple and Elementary Proof of a Theorem of Ingelstam. 54-58
• 
  William A. Beyer, Andrew Zardecki:
  The Early History of the Ham Sandwich Theorem. 58-61
• 
  Alexander R. Perlis:
  Roots Appear in Quanta. 61-63

Problems and Solutions

• 
  Shahin Amrahov:
  Problem 11054. 64
• 
  Razvan A. Satnoianu:
  Problem 11055. 64
• 
  John H. Lindsey II:
  Problem 11056. 64
• 
  : Problem 11057. 64
• 
  Óscar Ciaurri:
  Problem 11058. 64
• 
  Mark Bowron:
  Problem 11059. 64-65
• 
  Matthew E. Coppenbarger:
  Problem 11060. 65

Solutions

• 
  Peter Walker, Tom Zerger:
  The Centroid-Circumcenter Distance: 10948. 65-66
• 
  Leroy Quet, et al.:
  Functionally Related Convergents: 10953. 66-67
• 
  Razvan A. Satnoianu, Isaac Sofair:
  More Triangle Inequalities: 10955. 67-69
• 
  George Lamb, Stephen J. Herschkorn:
  Hypergeometric and Other Representations: 10959. 69-71
• 
  Mihály Bencze, Li Zhou:
  Cosine Inequalities: 10962. 71

Editor's Corner

• 
  Arnold Ostebee:
  Telegraphic Reviews. 82-84

Volume 111, Number 2, February 2004

• 
  Susan Landau:
  Polynomials in the Nation's Service: Using Algebra to Design the Advanced Encryption Standard. 89-117
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  Isoperimetric and Isoparametric Problems. 118-136
• 
  Charles Radin:
  Orbits of Orbs: Sphere Packing Meets Penrose Tilings. 137-149

Notes

• 
  Fabrizio Zanello:
  When Are There Infinitely Many Irreducible Elements in a Principal Ideal Domain? 150-152
• 
  David Avis, Bohdan Kaluzny:
  Solving Inequalities and Proving Farkas's Lemma Made Easy. 152-157
• 
  Suk-Geun Hwang:
  Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices. 157-159
• 
  Michael Schmitt:
  New Designs for the Descartes Rule of Signs. 159-164

Problems and Solutions

• 
  Wu Wei Chao:
  Problem 11061. 165
• 
  Kenneth Schilling:
  Problem 11062. 165
• 
  Slavko Simic:
  Problem 11063. 165
• 
  John E. Wetzel:
  Problem 11064. 165
• 
  Douglas B. Tyler:
  Problem 11065. 166
• 
  Sebastian M. Cioaba:
  Problem 11066. 166
• 
  George Lamb:
  Problem 11067. 166
• 
  Correction: 11034. 166
• 
  Donald E. Knuth, Robin Chapman:
  Fibonacci in Complex Camouflage: 10858. 166-167
• 
  Jeffrey C. Lagarias, Eric M. Rains, Neil J. A. Sloane, Nasha Komanda:
  The EKG Sequence: 10927. 167-168
• 
  Paul Schweitzer, Xiaoshen Wang, et al.:
  Too Much Commuting: 10930. 168-169
• 
  Robert DeSario, LeRoy Wenstrom:
  Invertible Shuffles: 10931. 169-170
• 
  Paul Lescott, Tom Jager:
  A Group Determined by Relations?: 10933. 170-171
• 
  David G. Wagner, Patrick Corn, Li Zhou:
  A Cyclotomic Sum: 10937. 171-172
• 
  Victor Alexandrov, Knut Dale:
  Using Stokes's Theorem on the Sphere: 10957. 172

Volume 111, Number 3, March 2004

• 
  Robert E. Megginson:
  Yueh-Gin Gung and Dr. Charles Y. Hu Award to T. Christine Stevens for Distinguished Service to Mathematics. 185-188
• 
  Alan Edelman, Gilbert Strang:
  Pascal Matrices. 189-197
• 
  William Ingram, William S. Mahavier:
  Interesting Dynamics and Inverse Limits in a Family of One-Dimensional Maps. 198-215
• 
  Jaume Paradís, Josep Pla, Pelegrí Viader:
  Fermat and the Quadrature of the Folium of Descartes. 216-229
• 
  Detlef Gronau:
  The Spiral of Theodorus. 230-237
• 
  Leslie Blackwell Galen:
  Putting Fractions in Their Place. 238-242

Notes

• 
  Tsuneo Ishikawa, Nobuhiko Ishida, Yoshito Yukimoto:
  On Prime Factors of. 243-245
• 
  Lourens M. Pretorius, Konrad J. Swanepoel:
  An Algorithmic Proof of the Motzkin-Rabin Theorem on Monochrome Lines. 245-251
• 
  Martin Engman:
  A Note on Isometric Embeddings of Surfaces of Revolution. 251-255
• 
  T. Y. Lam:
  On Subgroups of Prime Index. 256-258

Problems and Solutions

• 
  Herbert S. Wilf:
  Problem 11068. 259
• 
  Péter Ivády:
  Problem 11069. 259
• 
  Roberto Tauraso:
  Problem 11070. 259
• 
  Emeric Deutsch:
  Problem 11071. 259
• 
  George Lamb:
  Problem 11072. 259
• 
  Vicentiu D. Radulescu:
  Problem 11073. 260
• 
  Dimiter Skordev:
  Problem 11074. 260

Solutions

• 
  Roland Bacher, Robin Chapman, Reiner Martin:
  A Determinant of Indeterminates: 10859. 260-261
• 
  Jürgen Groß, Götz Trenkler, Xiaoshen Wang:
  Product and Sum of Projections: 10917. 261-262
• 
  Christian Bey, Garth Isaak:
  Maximum Antichains of Sets of Distinct Sizes: 10932. 262-263
• 
  Walther Janous, J. P. V. Abad:
  Maximum Antichains in the Divisor Lattice: 10942. 263
• 
  Calin Popescu, et al.:
  A Divisibility Result: 10943. 264
• 
  Jeffrey C. Lagarias, Walther Janous:
  A Generous Bound for Divisor Sums: 10949. 264-265
• 
  David Callan, M. A. Prasad:
  Counting a Set of Rooted Trees: 10952. 265-266
• 
  Brian Conrad, Gheorge Simion, Patrick Corn:
  Pi and Rationals: 10961. 266

Volume 111, Number 4, April 2004

• 
  Roe Goodman:
  Alice through Looking Glass after Looking Glass: The Mathematics of Mirrors and Kaleidoscopes. 281-298
• 
  Geoffrey R. Grimmett:
  Stochastic Apportionment. 299-307
• 
  Pirooz Mohazzabi, Thomas A. Fournelle:
  Evaluation of Ill-Behaved Power Series. 308-321
• 
  Curtis D. Bennett, Andrew M. W. Glass, Gábor J. Székely:
  Fermat's Last Theorem for Rational Exponents. 322-329
• 
  Bruce C. Berndt, C. A. Reddi:
  Two Exams Taken by Ramanujan in India. 330-339

Notes

• 
  Asuman Aksoy, Mario Martelli:
  The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem. 340-347
• 
  Dov Samet, Iddo Samet, David Schmeidler:
  One Observation behind Two-Envelope Puzzles. 347-351
• 
  Emmanuel Kowalski:
  On the "Reducibility" of Arctangents of Integers. 351-354
• 
  Paul Monsky:
  Kepler's First Law: A Remark. 355-356
• 
  Hervé Perdry:
  An Elementary Proof of Krull's Intersection Theorem. 356-357
• 
  Jacob Mostovoy:
  Lattices in ℂ and Finite Subsets of a Circle. 357-360

Problems and Solutions

• 
  Götz Trenkler:
  Problem 11075. 361
• 
  Joel Zinn:
  Problem 11076. 361
• 
  Gheorge Costovici:
  Problem 11077. 361
• 
  Donald E. Knuth:
  Problem 11078. 361
• 
  Brian Cook, James Whitenton:
  Problem 11079. 361-362
• 
  Razvan A. Satnoianu:
  Problem 11080. 362
• 
  Stephen Morse:
  Problem 11081. 362

Solutions

• 
  Marc Chamberland, et al.:
  A Sequence of Composite Numbers: 10947. 362-363
• 
  Sung Soo Kim, Li Zhou:
  A Sticky Problem: 10951. 363-364
• 
  John McCarthy, Lee Badger, Marc Williams:
  The Tower of Stanford: 10956. 364-365
• 
  Oliver Eng, Li Zhou:
  Sliding Dominoes: 10960. 365-366
• 
  M. L. Glosser, J. A. Grzesik:
  A Nontrivial Zero.: 11020. 366-367
• 
  Vicentiu D. Radulescu, Richard Stong:
  A Limit Problem: 11024. 367-368

Volume 111, Number 5, May 2004

• 
  Donald G. Saari:
  Geometry of Chaotic and Stable Discussions. 377-393
• 
  Maya Mohsin Ahmed:
  How Many Squares Are There, Mr. Franklin?: Constructing and Enumerating Franklin Squares. 394-410
• 
  Barbara S. Edwards, Michael B. Ward:
  Surprises from Mathematics Education Research: Student (Mis)use of Mathematical Definitions. 411-424

Notes

• 
  Jeroen Spandaw:
  Dissecting Cuboids into Cuboids. 425-429
• 
  Hirofumi Tsumura:
  An Elementary Proof of Euler's Formula for ζ(2m). 430-431
• 
  Grzegorz Rzadkowski:
  A Short Proof of the Explicit Formula for Bernoulli Numbers. 432-434
• 
  Raymond T. Boute:
  Moving a Rectangle around a Corner: Geometrically. 435-437
• 
  Christoph Leuenberger:
  An Old Friend Revisited. 437-439

Problems and Solutions

• 
  Wu Wei Chao:
  Problem 11082. 440
• 
  William P. Wardlaw:
  Problem 11083. 440
• 
  H. A. ShahAli:
  Problem 11084. 440
• 
  Matthias Beck, Jesús A. De Loera, Mike Develin, Julian Pfeifle:
  Problem 11085. 440
• 
  Stephen C. Locke:
  Problem 11086. 440-441
• 
  Michael Golomb:
  Problem 11087. 441
• 
  Richard Holzsager:
  Problem 11088. 441

Solutions

• 
  Robin Chapman, Nicholas Singer:
  Eigenvalues of a Bidiagonal Matrix: 10958. 441
• 
  Paul Deiermann, Cape Girardeau, Joseph Chalmers, George Lamb:
  An Application of the Mellin Transform: 10963. 441-443
• 
  Douglas B. West, Csaba Megyeri:
  Adjacency Matrices That Are Incidence Matrices: 10967. 443
• 
  Stephen C. Locke, Philip D. Straffin:
  The Game of Pathos: 10968. 443-444
• 
  Vitaly I. Voloshin, José Heber Nieto, Edward R. Scheinerman, Robin Chapman:
  Plucking Stirling Numbers from Trees: 10976. 444-445
• 
  Carl Axness, Bert Kerr, Jean-François Chamayou:
  Incomplete Gamma and Error Functions: 10977. 445-447
• 
  Donald E. Knuth, et al.:
  Some Bernstein Polynomials: 10985. 447

Volume 111, Number 6, June - July 2004

• 
  David E. Zitarelli:
  The Origin and Early Impact of the Moore Method. 465-486
• 
  Henry Cohn:
  Projective Geometry over and the Gaussian Binomial Coefficients. 487-495
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  A Fresh Look at the Method of Archimedes. 496-508
• 
  Casey Mann:
  Heesch's Tiling Problem. 509-517

Notes

• 
  Gilbert Helmberg:
  A Construction Concerning. 518-520
• 
  Kehe Zhu:
  Translating Inequalities between Hardy and Bergman Spaces. 520-525
• 
  Xiaoshen Wang:
  A Simple Proof of Descartes's Rule of Signs. 525-526
• 
  Sam B. Nadler Jr.:
  Another Proof That R³ Has No Square Root. 527-528
• 
  Steven H. Weintraub:
  An Interesting Recursion. 528-530
• 
  Gregory P. Dresden:
  On the Middle Coefficient of a Cyclotomic Polynomial. 531-533

Problems and Solutions

• 
  Sun Soo Kim:
  Problem 11089. 534
• 
  Florian Luca:
  Problem 11090. 534
• 
  David Callan:
  Problem 11091. 534
• 
  Arturo Magidin:
  Problem 11092. 534-535
• 
  Richard Bagby:
  Problem 11093. 535
• 
  Michel Bataille:
  Problem 11094. 535
• 
  Vasile Mihai:
  Problem 11095. 535

Solutions

• 
  H. A. ShahAli, Hamza Ahmad:
  Graceful Permutations Revisited: 10964. 535-536
• 
  Jean-Marie De Koninck, Stefan Gubo:
  When the Totient Is the Product of the Squared Prime Divisors: 10966. 536
• 
  Richard P. Stanley, O. P. Lossers:
  Comparing Odd Parts in Conjugate Partitions: 10969. 536-539
• 
  C. P. Rupert, Richard Stong:
  The First Fibonacci Number Divisible by a Prime p: 10971. 539-540
• 
  Tim Ferguson, M. D. Frederick, Lenny Jones, Stephen M. Gagola Jr.:
  The LCM of the Parts of a Partition: 10972. 540-541
• 
  Emeric Deutsch, Julio Kuplinsky, Tina Garrett:
  Enumeration of Permutations by Disorder: 10975. 541

Volume 111, Number 7, August - September 2004

• 
  Joan R. Leitzel:
  The 2003 James R. C. Leitzel Lecture: Mathematics' Response to Issues in Higher Education. 549-558
• 
  Reinhard Diestel:
  On Infinite Cycles in Graphs: Or How to Make Graph Homology Interesting. 559-571
• 
  Torsten Ekedahl, Dan Laksov:
  Two "Generic" Proofs of the Spectral Mapping Theorem. 572-585
• 
  Federico Ardila:
  The Number of Halving Circles. 586-591

Notes

• 
  Darko Veljan:
  Geometry and Convexity of cos √x. 592-595
• 
  Bau-Sen Du:
  A Simple Proof of Sharkovsky's Theorem. 595-599
• 
  Tyler Jarvis, James Tanton:
  The Hairy Ball Theorem via Sperner's Lemma. 599-603
• 
  Kenzi Satô:
  Some Subgroups of Isomorphic to the Free Product. 603-607

The Evolution of...

•