The American Mathematical Monthly, Volume 114

Volume 114, Number 1, January 2007

• 
  Peter Maier, Werner Nickel:
  Attainable Patterns in Alien Tiles. 1-13
• 
  Tanya Leise, Andrew Cohen:
  Nonlinear Oscillators at Our Fingertips. 14-28
• 
  Dave Auckly:
  Solving the Quartic with a Pencil. 29-39
• 
  Donatella Merlini, Renzo Sprugnoli, M. Cecilia Verri:
  The Method of Coefficients. 40-57

Notes

• 
  William F. Ford, James A. Pennline:
  When Does Convergence in the Mean Imply Uniform Convergence? 58-60
• 
  Sime Ungar:
  The Koch Curve: A Geometric Proof. 61-66
• 
  Dong-Soo Kim, Young Ho Kim:
  A Characterization of Ellipses. 66-70
• 
  Jonathan M. Borwein:
  A Class of Dirichlet Series Integrals. 70-76

Problems and Solutions

• 
  Donald E. Knuth:
  Problem 11264. 77
• 
  Steve Butler, Jia Mao:
  Problem 11265. 77
• 
  Marian Tetiva:
  Problem 11266. 77
• 
  Eugene A. Herman:
  Problem 11267. 77
• 
  M. L. Glasser:
  Problem 11268. 78
• 
  Hervé Moulin:
  Problem 11269. 78
• 
  Sergey Sadov:
  Problem 11270. 78

Solutions

• 
  David Beckwith:
  An Accidental Repetition of the All-Ones Problem: 10851. 78-79
• 
  Tom M. Apostol, et al.:
  Summing the Initial Inverted Powers: 11128. 79-80
• 
  M. L. Glasser, Richard Stong:
  An Elementary Integral: 11148. 80-81
• 
  Mircea Ivan, Ioan Rasa, M. A. Prasad:
  Limit with Nested Logs: 11149. 81
• 
  Paul Bracken, Michael Goldenberg, Mark Kaplan:
  A Nonlinear Recurrence: 11153. 81-82
• 
  Hillel Gauchman, et al.:
  Square Root Inequality: 11157. 82-83
• 
  Greg Oman, Michael W. Botsko:
  Isomorphic Rings of Functions: 11166. 83
• 
  Mohammad Hossein Mehrabi, O. P. Lossers:
  A Gamma Function Inequality: 11169. 83-84
• 
  Slavko Simic, et al.:
  Maximum Real Part of a Zero of a Polynomial: 11184. 84

Reviews

• 
  Fernando Q. Gouvêa:
  A First Course in Modular Forms by Fred Diamond; Jerry Shurman. 85-90
• 
  Daniel J. Velleman:
  Editor's Endnotes. 91

Volume 114, Number 2, February 2007

• 
  Richard K. Guy:
  The Lighthouse Theorem, Morley & Malfatti: A Budget of Paradoxes. 97-141
• 
  Po-Ru Loh:
  Stepping to Infinity Along Gaussian Primes. 142-151

Notes

• 
  Bau-Sen Du:
  A Simple Proof of Sharkovsky's Theorem Revisited. 152-155
• 
  Gwen Spencer, Francis Edward Su:
  The LSB Theorem Implies the KKM Lemma. 156-159
• 
  Sam B. Nadler Jr., Donna M. Zitney:
  Pointwise Products of Uniformly Continuous Functions on Sets in the Real Line. 160-163

Problems and Solutions

• 
  Iliya Bluskov:
  Problem 11271. 164
• 
  Vasile Mihai:
  Problem 11272. 164
• 
  Marian Tetiva:
  Problem 11273. 164-165
• 
  Donald E. Knuth:
  Problem 11274. 165
• 
  Michael S. Becker:
  Problem 11275. 165
• 
  Eugene A. Herman:
  Problem 11276. 165

Solutions

• 
  Vicentiu D. Radulescu, Richard Stong:
  Exponential Growth of a Solution: 11137. 165-166
• 
  George Lamb, J. A. Grzesik:
  A Quadrature on a Sphere: 11159. 167
• 
  Paolo Perfetti, et al.:
  Series with Sines: 11162. 167-168
• 
  Vicentiu D. Radulescu, et al.:
  Ginzburg-Landau Energy: 11167. 168-170
• 
  Suat Namli, O. P. Lossers:
  A Functional Equation with Exponential Solutions: 11180. 170-171
• 
  Grahame Bennett, Eugene A. Herman:
  Apply Hölder: 11202. 171

Reviews

• 
  Gerald B. Folland:
  Analysis I: Convergence, Elementary Functions by Roger Godement; Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions by Roger Godement. 172-176

Volume 114, Number 3, March 2007

• 
  Amy Cohen-Corwin:
  Yueh-Gin Gung and Dr. Charles Y. Hu Award to Lee Lorch for Distinguished Service to Mathematics. 181-182
• 
  Robyn Curtis, Marcel Steiner:
  Configuration Spaces of Planar Pentagons. 183-201
• 
  Katherine Socha:
  Circles in Circles: Creating a Mathematical Model of Surface Water Waves. 202-216
• 
  Anders Claesson, T. Kyle Petersen:
  Conway's Napkin Problem. 217-231
• 
  Dante Manna, Victor H. Moll:
  A Simple Example of a New Class of Landen Transformation. 232-241

Notes

• 
  Michael W. Botsko:
  Exactly Which Bounded Darboux Functions Are Derivatives? 242-246
• 
  Mark Levi:
  Riemann Mapping Theorem by Steepest Descent. 246-251
• 
  David H. Armitage:
  Entire Functions That Tend to Zero on Every Line. 251-256
• 
  Mark A. Pinsky:
  Stirling's Formula via the Poisson Distribution. 256-258

Problems and Solutions

• 
  Prithwijit De:
  Problem 11277. 259
• 
  Slavko Simic:
  Problem 11278. 259
• 
  Vitaly Stakhovsky:
  Problem 11279. 259
• 
  Harris Kwong:
  Problem 11280. 259
• 
  Max A. Alekseyev, Emeric Deutsch:
  Problem 11281. 259
• 
  Dragomir Z. Dkovic, Kaiming Zhao:
  Problem 11282. 260
• 
  John Abbot, Umberto Zannier:
  Problem 11283. 260

Solutions

• 
  Stephen B. Gray, Thomas McMillan, Xiaoshen Wang:
  Stepping to Regularity: 10923. 260-261
• 
  Kent D. Boklan, Michael Avidon:
  Heronian Triangles: 11134. 261-262
• 
  Ernst Schulte-Geers, Karl David:
  An Identity Involving Rooted Forest: 11144. 262-264
• 
  Yongge Tian, Eugene A. Herman:
  Matrix Systems with the Same Sets: 11146. 264
• 
  Emeric Deutsch, O. P. Lossers:
  Peaks in Dyck Paths: 11150. 264-265
• 
  Donald E. Knuth, O. P. Lossers:
  Partitions of a Circular Set: 11151. 265-266
• 
  Kent Holing, Michael Avidon:
  Indivisibility of the Sum of Squares: 11154. 266

Reviews

• 
  John Stillwell:
  God Created the Integers by Stephen Hawking. 267-271

Volume 114, Number 4, April 2007

• 
  Alberto A. Martínez:
  Euler's "Mistake"? The Radical Product Rule in Historical Perspective. 273-285
• 
  Christopher Francese, David Richeson:
  The Flaw in Euler's Proof of His Polyhedral Formula. 286-296
• 
  Gopala Krishna Srinivasan:
  The Gamma Function: An Eclectic Tour. 297-315
• 
  Bennett Chow, David Glickenstein:
  Semidiscrete Geometric Flows of Polygons. 316-328
• 
  Colin Adams, Frank Morgan, John M. Sullivan:
  When Soap Bubbles Collide. 329-337

Notes

• 
  Arthur T. Benjamin, Gregory P. Dresden:
  A Combinatorial Proof of Vandermonde's Determinant. 338-341
• 
  Michael A. Allen:
  Evaluation of Some Improper Integrals Involving Hyperbolic Functions. 341-343
• 
  Robin Pemantle, Carsten Schneider:
  When Is 0.999... Equal to 1? 344-350
• 
  Brendan Foreman:
  Ghys's Theorem and Semi-Osculating Conics of Planar Curves. 351-356
• 
  Gilbert Helmberg:
  An Absolutely Continuous Function in L1 (R) W1, 1 (R). 356-357

Problems and Solutions

• 
  Greg Oman:
  Problem 11284. 358
• 
  Yakub N. Aliyev:
  Problem 11285. 358
• 
  Marc LeBrun, David L. Applegate, Neil J. A. Sloane:
  Problem 11286. 358
• 
  Stephen J. Herschkorn:
  Problem 11287. 359
• 
  Christopher J. Hillar, Troels Windfeldt:
  Problem 11288. 359
• 
  Oleh Faynshteyn:
  Problem 11289. 359
• 
  Cezar Lupu, Tudorel Lupu:
  Problem 11290. 359

Solutions

• 
  Jonathan Sondow, Richard Stong:
  Choice Bounds: 11132. 359-360
• 
  Paul Bracken, Heinz-Jürgen Seiffert:
  An Integral Inequality: 11133. 360-361
• 
  Donald E. Knuth, Roberto Tauraso:
  A Combinatorial Maximum: 11142. 361-362
• 
  Richard P. Stanley, et al.:
  Inverting a Matrix of Striling Numbers: 11156. 362
• 
  Emeric Deutsch, et al.:
  Compositions without Common Factors: 11161. 363
• 
  Michel Bataille, Richard Stong:
  Counting Lattice Quadrilaterals Tangent to an Ellipse: 11163. 363-364
• 
  José Luis Díaz-Barrero, Ulrich Abel, Mircea Ivan:
  A Recurrent Identify: 11164. 364-365

Reviews

• 
  John P. D'Angelo:
  Geometric Function Theory: Explorations in Complex Analysis by Steven G. Krantz. 366-370

Volume 114, Number 5, May 2007

• 
  Yuval Peres, Oded Schramm, Scott Sheffield, David Bruce Wilson:
  Random-Turn Hex and Other Selection Games. 373-387
• 
  Tom M. Apostol, Mamikon A. Mnatsakanian:
  Unwrapping Curves from Cylinders and Cones. 388-416
• 
  Graham Everest, Shaun Stevens, Duncan Tamsett, Thomas Ward:
  Primes Generated by Recurrence Sequences. 417-431

Notes

• 
  J. W. Neuberger:
  The Continuous Newton's Method, Inverse Functions, and Nash-Moser. 432-437
• 
  Anthony Mendes:
  A Note on Alternating Permutations. 437-440
• 
  Michael Kerckhove, Gary Lawlor:
  The Circle and the Cycloid: A Surprising Link. 441-443
• 
  Jack Ohm:
  A Matrix Approach to Zero-Divisors in R[x]. 444-450

Problems and Solutions

• 
  Richard Jerrard, John E. Wetzel:
  Problem 11291. 451
• 
  David Callan:
  Problem 11292. 451
• 
  Sergey Sadov:
  Problem 11293. 451
• 
  John Zucker, Ross C. McPhedran:
  Problem 11294. 452
• 
  Stefano Siboni:
  Problem 11295. 452
• 
  Saïd Amghibech:
  Problem 11296. 452
• 
  Marian Tetiva:
  Problem 11297. 452

Solutions

• 
  Bogdan Nica, Saïd Amghibech:
  Similarities of Euclidean Space: 11124. 452-453
• 
  Alexander Dubinov, Irina Dubinova:
  Closed Form Closure: 11143. 453
• 
  David Beckwith, Harris Kwong:
  Prime Powers Dividing a Factorial: 11158. 453-454
• 
  Marc Chamberland, C. R. Pranesachar:
  Fermat to the Rescue: 11160. 454
• 
  Yogesh More, Robin Chapman:
  The Sum of Catalan Numbers, Modulo 3: 11165. 454-455
• 
  Kent Holing, et al.:
  Properties of Pythagorean Triples: 11168. 455-456
• 
  Emeric Deutsch, Stephen C. Locke:
  Dissecting a Polygon: 11170. 456-457
• 
  Heinz-Jürgen Seiffert:
  Familiar Identities in Disguise: 11172. 457-458

Reviews

• 
  David M. Bressoud:
  Making Transcendence Transparent by B. Burger; Robert Tubbs. 459-461
• 
  Mark Schwartz:
  Conics by Keith Kendig. 461-464

Volume 114, Number 6, June - July 2007

• 
  Brian S. Thomson:
  Rethinking the Elementary Real Analysis Course. 469-490
• 
  Andrew J. Hetzel, Jay S. Liew, Kent E. Morrison:
  The Probability That a Matrix of Integers Is Diagonalizable. 491-499
• 
  Brody Dylan Johnson:
  The Nonholonomy of the Rolling Sphere. 500-508
• 
  Dierk Schleicher:
  Hausdorff Dimension, Its Properties, and Its Surprises. 509-528

Notes

• 
  Ling-Ling Shi, Hao Pan:
  A q-Analogue of Wolstenholme's Harmonic Series Congruence. 529-531
• 
  Jürgen Bliedtner, Peter A. Loeb:
  A Local Maximal Function Simplifying Measure Differentiation. 532-536
• 
  Boris Adamczewski, Yann Bugeaud:
  A Short Proof of the Transcendence of Thue-Morse Continued Fractions. 536-540
• 
  Joseph Bak, Pisheng Ding, Donald Newman:
  Extremal Points, Critical Points, and Saddle Points of Analytic Functions. 540-546

Problems and Solutions

• 
  Jakob Jonsson:
  Problem 11298. 547
• 
  Pablo Fernández Refolio:
  Problem 11299. 547
• 
  Ulrich Abel:
  Problem 11300. 547
• 
  Finbarr Holland:
  Problem 11301. 547
• 
  Horst Alzer:
  Problem 11302. 547
• 
  Mohammad Farrokhi D. G.:
  Problem 11303. 548
• 
  Teodora-Liliana Radulescu:
  Problem 11304. 548

Solutions

• 
  M. N. Deshpande, J. P. Shiwalkar, et al.:
  Two Heads Are Better than One: 11173. 548-549
• 
  Jon Louis Bentley, Colin L. Mallows, Richard Stong:
  Learning from Experience: 11178. 549-550
• 
  David Beckwith, Li Zhou:
  A Determinant by Möbius Inversion: 11179. 550
• 
  Shahin Amrahov, Nicholas Singer:
  Perfect Powers in an Arithmetic Progression: 11182. 550-551
• 
  David Beckwith, Vadim Ponomarenko, Rob Pratt:
  Building Two Piles of Equal Height: 11183. 551-552
• 
  Rainer Brück, Robin Chapman:
  When Does It Converge: 11185. 552-554
• 
  Li Zhou, Christopher Carl Heckman, Jerry Minkus, et al.:
  Tiling 4-Rowed Rectangles with Dominoes: 11187. 554-556

Reviews

• 
  Susan Jane Colley:
  Introduction to Plane Algebraic Curves by Ernst Kunz; Richard G. Belshoff. 557-561

Volume 114, Number 7, August - September 2007

• 
  Enrique A. González-Velasco:
  James Gregory's Calculus in the "Geometriœ Pars Universalis". 565-576
• 
  Roman Dwilewicz, Ján Minác, Andrew Schultz, John Swallow:
  Hilbert 90 for Biquadratic Extensions. 577-587
• 
  Arno Berger, Theodore P. Hill:
  Newton's Method Obeys Benford's Law. 588-601
• 
  Jin Akiyama:
  Tile-Makers and Semi-Tile-Makers. 602-609
• 
  Byron L. Walden, Lesley A. Ward:
  A Harmonic Measure Interpretation of the Arithmetic-Geometric Mean. 610-622

Notes

• 
  Carlos A. Escudero, Agustí Reventós:
  An Interesting Property of the Evolute. 623-628
• 
  Jack Cook, Jonathan Lovett, Frank Morgan:
  Rotation in a Normed Plane. 628-632
•