The American Mathematical Monthly, Volume 116

Volume 116, Number 1, January 2009

• 
  Judith V. Grabiner:
  Why Did Lagrange "Prove" the Parallel Postulate? 3-18
• 
  Mike Paterson, Uri Zwick:
  Overhang. 19-44
• 
  Larry Goldstein:
  A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem. 45-60
• 
  José Ángel Cid, Rodrigo López Pouso:
  Does Lipschitz with Respect to x Imply Uniqueness for the Differential Equation y′ = f(x, y)? 61-66

Notes

• 
  Ed Scheinerman, Anton R. Schep:
  A Simple Complex Analysis and an Advanced Calculus Proof of the Fundamental Theorem of Algebra. 67-68
• 
  Natalia Casás Ferreño:
  Yet Another Proof of the Irrationality of √2. 68-69
• 
  Giovanni Panti:
  A General Lagrange Theorem. 70-74
• 
  Romeo Mestrovic:
  A Note on the Congruence (nd md) = (n m) (mod q). 75-77
• 
  Sheldon M. Ross:
  A Simple Solution to a Multiple Player Gambler's Ruin Problem. 77-81

Problems and Solutions

• 
  Raimond Struble:
  Problem 11404. 82
• 
  Ovidiu Furdui:
  Problem 11405. 82
• 
  A. A. Dzhumadildaeva:
  Problem 11406. 82
• 
  Erwin Just:
  Problem 11407. 82
• 
  Marius Cavachi:
  Problem 11408. 83
• 
  Paolo Perfetti:
  Problem 11409. 83
• 
  Omran Kouba:
  Problem 11410. 83

Solutions

• 
  Richard Jerrard, John E. Wetzel, Mark D. Meyerson:
  A Solid with the Rupert Property: 11291. 83-84
• 
  Pablo Fernández Refolio, Timothy Achenbach:
  An Infinite Product: 11299. 84
• 
  Ulrich Abel:
  A Bernstein Polynomial Integral: 11300. 84-85
• 
  Finbarr Holland, Byoung Tae Bae:
  A Quartic Inequality: - 11301. 85-86
• 
  Horst Alzer:
  A Series with Harmonic Numbers: 11302. 86-87
• 
  Teodora-Liliana Radulescu:
  Signed Series Terms: 11304. 87-88
• 
  Alexandru Rosoiu, Victor Pambuccian:
  An Inequality for Triangles: 11306. 88-89

Reviews

• 
  Erik Talvila:
  Review: A Garden of Integrals by Frank E. Burk. 90-94

Volume 116, Number 2, February 2009

• 
  Thomas L. Bartlow, David E. Zitarelli:
  Who Was Miss Mullikin? 99-114
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  A New Look at the So-Called Trammel of Archimedes. 115-133
• 
  Frank Morgan:
  Manifolds with Density and Perelman's Proof of the Poincaré Conjecture. 134-142
• 
  Joseph Bak, Pisheng Ding:
  Shape Distortion by Analytic Functions. 143-150
• 
  Christian Haase, Josef Schicho:
  Lattice Polygons and the Number 2i + 7. 151-165

Notes

• 
  Stephen K. Lucas:
  Approximations to π Derived from Integrals with Nonnegative Integrands. 166-172
• 
  Juan Pablo Pinasco:
  New Proofs of Euclid's and Euler's Theorems. 172-174
• 
  Janusz Januszewski:
  A Note on Covering a Square of Side Length 2 + with Unit Squares. 174-178

Problems and Solutions

• 
  Alun Wyn-jones:
  Problem 11411. 179
• 
  Omran Kouba:
  Problem 11412. 179
• 
  Mihály Bencze:
  Problem 11413. 179
• 
  Marian Tetiva:
  Problem 11414. 179-180
• 
  Finbar Holland:
  Problem 11415. 180
• 
  Yaming Yu:
  Problem 11416. 180
• 
  Cezar Lupu:
  Problem 11417. 180

Solutions

• 
  Steve Butler, Jia Mao:
  Graphs with Few Edges, All in Short Cycles: 11265. 180-181
• 
  Marian Tetiva, Robin Chapman:
  Partitioning Values of a Polynomial into Sets of Equal Sum: 11266. 181-183
• 
  Eugene A. Herman, Richard Stong:
  Commuting Transformations: 11267. 183
• 
  Ovidiu Furdui, Vitaly Stakhovsky:
  An Inequality with Trig: 11308. 183-184
• 
  Roman Witula, Damian Slota, Arman Darbinyan, David Borwein:
  A Trig-Of-Trig Inequality: 11309. 184-185
• 
  Stephen J. Herschkorn:
  A Game with Coins and Balls: 11311. 185-186

Reviews

• 
  V. S. Varadarajan:
  Review: Introduction to Calculus and Classical Analysis by Omar Hijab. 187-190

Volume 116, Number 3, March 2009

• 
  Barbara Faires:
  Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2009 to Robert E. Megginson for Distinguished Service to Mathematics. 195-196
• 
  Alan H. Schoenfeld:
  Working with Schools: The Story of a Mathematics Education Collaboration. 197-217
• 
  Russell A. Gordon:
  Some Integrals Involving the Cantor Function. 218-227
• 
  Jerzy Kocik, Andrzej Solecki:
  Disentangling a Triangle. 228-237
• 
  Aaron Melman:
  Overshooting Properties of Newton-Like and Ostrowski-Like Methods. 238-250
• 
  Serge Troubetzkoy:
  Dual Billiards, Fagnano Orbits, and Regular Polygons. 251-260

Notes

• 
  Shirley Llamado Yap:
  The Poincaré Lemma and an Elementary Construction of Vector Potentials. 261-267
• 
  Emmanuel Preissmann, Maurice Mischler:
  Seating Couples around the King's Table and a New Characterization of Prime Numbers. 268-272
• 
  Amir Akbary, Zachary Friggstad:
  Superabundant Numbers and the Riemann Hypothesis. 273-275

Problems and Solutions

• 
  George Lamb:
  Problem 11418. 276
• 
  Vasile Mihai:
  Problem 11419. 276
• 
  Kent Holing:
  Problem 11420. 277
• 
  Sergio Falcón, Ángel Plaza:
  Problem 11421. 277
• 
  Christopher J. Hillar:
  Problem 11422. 277
• 
  Gregory Minton:
  Problem 11423. 277
• 
  Emeric Deutsch:
  Problem 11424. 277

Solutions

• 
  Donald E. Knuth, Richard Stong:
  Reversal by Swaps: 11264 [2007, 77]. 277-278
• 
  Cezar Lupu, Li Zhou:
  From Integral to Derivative: 11313 [2007, 744]. 279
• 
  Yakub N. Aliyev, Marian Tetiva:
  A Floor Equation: 11314 [2007, 744]. 279-281
• 
  Ovidiu Furdui, et al.:
  Convergence of an Improper Integral with Three Parameters: 11316 [2007, 745]. 281-283
• 
  David Beckwith, et al.:
  Sum of Digits: 11319 [2008, 835]. 283

Reviews

• 
  Philip D. Straffin:
  Mr. Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century by Alex D. D. Craik. 284-288

Volume 116, Number 4, April 2009

• 
  Michael F. Barnsley:
  Transformations between Self-Referential Sets. 291-304
• 
  B. Ross Barmish, Nigel Boston:
  Risk and Return Considerations in "The Weakest Link". 305-315
• 
  Hajrudin Fejzic, Chris Freiling, Dan Rinne:
  Descartes' Rule of Signs, Alternations of Data Sets, and Balanced Differences. 316-327
• 
  Douglas Drinen, Kathleen Grace Kennedy, William M. Priestley:
  An Optimization Problem with a Surprisingly Simple Solution. 328-341
• 
  Ethan D. Bloch:
  A Simple Proof of a Generalized No Retraction Theorem. 342-350

Notes

• 
  Bruce Solomon:
  Central Cross-Sections Make Surfaces of Revolution Quadric. 351-355
• 
  Idris David Mercer:
  On Furstenberg's Proof of the Infinitude of Primes. 355-356
• 
  Jerry J. Koliha:
  Mean, Meaner, and the Meanest Mean Value Theorem. 356-361
• 
  Giedrius Alkauskas:
  A Curious Proof of Fermat's Little Theorem. 362-364

Problems and Solutions

• 
  Erwin Just:
  Problem 11425. 365
• 
  M. L. Glasser:
  Problem 11426. 365
• 
  Viorel Bandila:
  Problem 11427. 365
• 
  Walter Blumberg:
  Problem 11428. 365
• 
  Cezar Lupu:
  Problem 11429. 365-366
• 
  He Yi:
  Problem 11430. 366
• 
  Finbarr Holland, Stephen Wills:
  Problem 11431. 366

Solutions

• 
  Marian Tetiva, Robin Chapman:
  Partitioning Values of a Polynomial into Sets of Equal Sum: 11266 [2007, 77]. 366-368
• 
  Sergey Sadov, Harris Kwong:
  The Determinant of a Spiral Matrix: 11270 [2007, 78]. 368-369
• 
  Iliya Bluskov:
  Covering the Chessboard with Sets of Non-Attacking Queens: 11271 [2007, 164]. 369-370
• 
  Sergey Sadov, Kim McInturff:
  Determinant of Another Spiral Matrix: 11293 [2007, 451]. 370-371
• 
  Jakob Jonsson, Annie Carter, David Callan:
  Oddly Triangulated Polygons: 11298 [2007, 547]. 371-372
• 
  Mohammad Farrokhi D. G., T. S. Michael:
  A Characterization of Permutation Matrices: 11303 [2007, 548]. 372

Reviews

• 
  James W. Vick:
  Review: Topology Now! by Robert Messer; Philip Straffin; Introduction to Topology: Pure and Applied by Colin Adams; Robert Franzosa. 373-375
• 
  Kristopher Tapp:
  Review: Differential Geometry and Its Applications by John Oprea. 375-377
• 
  Daniel J. Velleman:
  Editor's Endnotes. 378-382

Volume 116, Number 5, May 2009

• 
  Jonathan M. Borwein, Neil J. Calkin, Dante Manna:
  Euler-Boole Summation Revisited. 387-412
• 
  Mira Bhargava:
  Groups as Unions of Proper Subgroups. 413-422
• 
  Rick Mabry, Paul Deiermann:
  Of Cheese and Crust: A Proof of the Pizza Conjecture and Other Tasty Results. 423-438
• 
  Nieves Alamo, Carlos Criado:
  Parallel Transport and Thomas-Wigner Rotation. 439-446

Notes

• 
  Daniel Heath, I. M. Isaacs, John Kiltinen, Jessica Sklar:
  Symmetric and Alternating Groups Generated by a Full Cycle and Another Element. 447-451
• 
  Michael J. Evans, Paul D. Humke:
  Revisiting a Century-Old Characterization of Baire Class One, Darboux Functions. 451-455
• 
  Chris Bernhardt:
  A Proof of the Cayley-Hamilton Theorem. 456-457
• 
  Peter Wagner:
  A New Constructive Proof of the Malgrange-Ehrenpreis Theorem. 457-462

Problems and Solutions

• 
  Marian Tetiva:
  Problem 11432. 463
• 
  Marius Cavachi:
  Problem 11433. 463
• 
  Slavko Simic:
  Problem 11434. 463
• 
  Panagiote Ligouras:
  Problem 11435. 463
• 
  Yakub N. Aliyev:
  Problem 11436. 463-464
• 
  Tamás Erdélyi:
  Problem 11437. 464
• 
  David H. Bailey:
  Problem 11438. 464

Solutions

• 
  Marian Tetiva, Byron Schmuland:
  A Sequence of Partitions into Sets with Equal Sum: 11273 [2007, 164]. 464-465
• 
  Max A. Alekseyev, John Henry Steelman:
  Counting Permutations with Two Displacement Values: 11281 [2007, 259]. 465
• 
  John Abbot, John Wilkinson:
  Irreducible Polynomials from a Theorem of Fermat: 11283 [2007, 260]. 465-466
• 
  Greg Oman, Manuel Reyes:
  Rings That are Fields: 11284 [2007, 358]. 466
• 
  Marc LeBrun:
  Descending Dungeons: 11286 [2007, 358]. 466-467
• 
  Christopher J. Hillar, Saïd Amghibech:
  A Polynomial Identity: 11288 [2007, 359]. 468
• 
  David Callan, Robin Chapman:
  Divisibility of a Central Binomial Sum: 11292&11307 [2007, 451&640]. 468-470
• 
  Mohammad Farrokhi D. G., Tuomas Hytönen:
  The Prime Exponentiation of an Integer: 11315 [2007, 744]. 470

Reviews

• 
  Allen Holder:
  Understanding and Using Linear Programming by Jiří Matoušek; Bernd Gärtner; Introduction to Optimization by Pablo Pedregal. 471-476

Volume 116, Number 6, June-July 2009

• 
  Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra:
  Musical Actions of Dihedral Groups. 479-495
• 
  Julius B. Barbanel, Steven J. Brams, Walter Stromquist:
  Cutting a Pie Is Not a Piece of Cake. 496-514
• 
  Jack S. Calcut:
  Gaussian Integers and Arctangent Identities for π. 515-530

Notes

• 
  Kevin Beanland, James W. Roberts, Craig Stevenson:
  Modifications of Thomae's Function and Differentiability. 531-535
• 
  Ulrich Abel, Mircea Ivan:
  Over-Iterates of Bernstein's Operators: A Short and Elementary Proof. 535-538
• 
  Paul Levrie, Walter Daems:
  Evaluating the Probability Integral Using Wallis's Product Formula for π. 538-541
• 
  Gerald Kuba:
  Counting Fields of Complex Numbers. 541-546

Problems and Solutions

• 
  Stephen Herschkorn:
  Problem 11439. 547
• 
  Stefano Siboni:
  Problem 11440. 547
• 
  Yakub N. Aliyev:
  Problem 11441. 547
• 
  José Luis Díaz-Barrero, José Gibergans-Báguena:
  Problem 11442. 547-548
• 
  Eugen J. Ionascu:
  Problem 11443. 548
• 
  Marian Tetiva:
  Problem 11444. 548
• 
  H. A. ShahAli:
  Problem 11445. 548

Solutions

• 
  Donald E. Knuth, Julian L. Hook:
  Sums and Powers, Set Counting, and Coefficient Tracking: 11274 [2007, 165]. 548-549
• 
  Dragomir Z. Dokovic, Richard Stong:
  A Unipotent Matrix: 11282 [2007, 260]. 549-550
• 
  Vahan Mkrtchyan, Codrut Grosu:
  Disjoint Maximum-Sized Matchings: 11305 [2007, 640]. 550-551
• 
  Erwin Just, Tom Kezlan:
  An Exponential Condition for Commutativity: 11310 [2007, 641]. 551-552
• 
  David Callan, Marc Renault:
  Uniformly Distributed Valleys: 11312 [2007, 744]. 552-553
• 
  Michel Bataille, John Cade:
  From Quadrilateral to Trapezoid: 11317 [2007, 745]. 553-554

Reviews

• 
  Branko Grünbaum:
  The Symmetries of Things by John H. Conway; Heidi Burgiel; Chaim Goodman-Strauss. 555-562

Volume 116, Number 7, August-September 2009

• 
  Nayandeep Deka Baruah, Bruce C. Berndt, Heng Huat Chan:
  Ramanujan's Series for 1/π: A Survey. 567-587
• 
  Greg Martin, Erick B. Wong:
  Almost All Integer Matrices Have No Integer Eigenvalues. 588-597
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  New Insight into Cycloidal Areas. 598-611
• 
  Richard W. Kenyon, Peter Winkler:
  Branched Polymers. 612-628

Notes

• 
  Shui-Hung Hou:
  On a Theorem of Abel. 629-630
• 
  Jonathan Sondow:
  Ramanujan Primes and Bertrand's Postulate. 630-635
• 
  Shawn Hedman, David Rose:
  Light Subsets of N with Dense Quotient Sets. 635-641
• 
  Juan Sabia, Susana Tesauri:
  The Least Prime in Certain Arithmetic Progressions. 641-643
• 
  Oliver Deiser:
  A Simple Continuous Bijection from Natural Sequences to Dyadic Sequences. 643-646

Problems and Solutions

• 
  Christopher J. Hillar:
  Problem 11446. 647
• 
  Ovidiu Furdui, Campia Turzii:
  Problem 11447. 647
• 
  Wei-Dong Jiang:
  Problem 11448. 647
• 
  Michel Bataille:
  Problem 11449. 647
• 
  Cosmin Pohoata:
  Problem 11450. 647
• 
  Greg Oman:
  Problem 11451. 648
• 
  Donald E. Knuth:
  Problem 11452. 648

Solutions

•