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Number 1 / JANUARY 1993......Page 1 Finkel Letter......Page 3 COMMENTS......Page 4 The Seventy-Fifth Anniversary Celebration I G. BALEY PRICE......Page 5 An Axiomatic Approach to the Integral/LEONARD GILLMAN......Page 17 Versatile Coins / ISTVAN SZALKAI and DAN VELLEMAN......Page 27 Two-Year Magazine Subscription Rates / UNDERWOOD DUDLEY......Page 35 On Seeing Progressions of Constant Cross Ratio / R. J. DUFFIN......Page 39 100 Years of Monthly Editors / JOHN EWING......Page 49 Quotients of Primes / DAVID HOBBY and D. M. SILBERGER......Page 51 Pathological Functions for Newton's Method / GEORGE C. DONOVAN, ARNOLD R. MILLER, and TIMOTHY J. MORELAND......Page 54 FEATURES......Page NOTES......Page 60 A Short Proof of a Theorem of Erdos and Mordell / ANDRE AVEZ......Page 61 The Computer Solves the Three Tower Problem / ARTHUR ENGEL......Page 63 A Linear Algebra Approach to Cyclic Extensions in Galois Theory / EVAN G. HOUSTON......Page 65 THE AUTHORS......Page 68 LETTERS......Page 70 When Does a Polynomial Over a Finite Field Permute the Elements of Field?, II/RUDOLF LIDL and GARY L. MULLEN......Page 72 PROBLEMS AND SOLUTIONS......Page 76 Iteration of Rational Functions by Alan F. Beardon / ROBERT L. DEVANEY......Page 91 TELEGRAPHIC REVIEWS......Page 95 Number 2 / FEBRUARY 1993......Page 103 CONTENTS......Page 105 COMMENTS......Page 106 Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Henry O. Pollak / RAMANATHAN GNANADESIKAN and HENRY J. LANDAU......Page 107 John Marvin Colaw: and The American Mathematical Monthly / JOHN D. MAXWELL......Page 109 Newton and the Transmutation of Force / TRISTAN NEEDHAM......Page 111 A Note on Diophantine Representations / CHRISTOPH BAXA......Page 130 Recurrence of Simple Random Walk in the Plane / TERENCE R. SHORE and DOUGLAS B. TYLER......Page 136 Pick's Theorem / BRANKO GRUNBAUM AND G. C. SHEPHARD......Page 142 Mathematics for Liberal Arts Students / ALBERT W. BRIGGS, JR.......Page 154 Sequences with Large Numbers of Prime Value / Ulrich Abel, Hartmut Siebert......Page 159 Regular Simplices in Spaces of Constant Curvature / Horst Martini......Page 161 A Simple Example of Little Big Set / John K. Williams......Page 164 PICTURE PUZZLE......Page 167 THE AUTHORS......Page 168 LETTERS......Page 170 A mod-n Ackermann Function, or What's So Special About 1969? / JON FROEMKE AND JERROLD W. GROSSMAN......Page 172 PROBLEMS AND SOLUTIONS......Page 176 How to Read and Do Proofs, by Daniel Solow / M. F. JANOWITZ......Page 189 TELEGRAPHIC REVIEWS......Page 192 Number 3 / MARCH 1993......Page 200 CONTENTS......Page 202 COMMENTS......Page 203 Szeged in 1934/ EDGAR R. LORCH......Page 204 Tarski's High School Identities / STANLEY BURRIS and SIMON LEE......Page 216 Aperiodic Chaotic Orbits / STEVEN N. MACEACHERN and L. MARK BERLINER......Page 222 Bricklaying and the Hermite Normal Form / WILLIAM J. GILBERT......Page 227 A Characterization of Inner Product Spaces / NEIL FALKNER......Page 231 Polar Area Is the Average of Strip Areas / GILBERT STRANG......Page 235 Counting Critical Points of Real Polynomials in Two Variables / ALAN DURFEE, NATHAN KRONENFELD, HEIDI MUNSON, JEFF ROY, and INA WESTBY......Page 240 Separation of the Zeros of Polynomials / Peter Walker......Page 257 A Short Proof of Jacobi's Formula for the Number of Representations of an Integer as a Sum of Four Squares / George E. Andrews, Shalosh B. Ekhad, Doron Zeilberger......Page 259 An Elementary Proof of Hilbert's Inequality / Krzysztof Oleszkiewicz......Page 261 A Note on Fubini's Theorem / Camille Debieve......Page 266 PICTURE PUZZLE......Page 267 THE AUTHORS......Page 268 LETTERS......Page 270 Parker's Permutation Problem Involves the Catalan Numbers......Page 272 PROBLEMS AND SOLUTIONS......Page 275 Ethnomathematics: A Multicultural View of Mathematical Ideas by Marcia Ascher / JUDITH V. GRABINER......Page 289 TELEGRAPHIC REVIEWS......Page 294 Number 4 / APRIL 1993......Page 302 CONTENTS......Page 304 COMMENTS......Page 305 Taxicabs and Sums of Two Cubes / JOSEPH H. SILVERMAN......Page 306 The Evil Twin Strategy for a Football Pool/JOSEPH DESTEFANO, PETER DOYLE, and J. LAURIE SNELL......Page 316 Six, Lies, and Calculators / R. M. CORLESS......Page 319 What Is a Napierian Logarithm? / RAYMOND AYOUB......Page 326 The Tyranny of Tests / PETER HILTON......Page 340 A Really Trivial Proof of the Lucas-Lehmer Test / J. W. BRUCE......Page 345 Pascal's Matrices / GREGORY S. CALL and DANIEL J. VELLEMAN......Page 347 Symmetries of the Cube and Outer Automorphisms of S_6 / THOMAS A. FOURNELLE......Page 352 Isogonal Configurations / TIMOTHY A. MURDOCH......Page 356 PSL2(Z) = Z2 * Z3 / Roger C. Alperin......Page 360 Generators for the Algebra of Symmetric Polynomials / D. G. Mead......Page 361 A Formula and a Proof of the Infinitude of the Primes / Michael Rubinstein......Page 363 PICTURE PUZZLE......Page 368 THE AUTHORS......Page 369 LETTERS......Page 371 Are There only Finitely Many Binomial Coefficients with Positive Deficiency?......Page 373 PROBLEMS AND SOLUTIONS......Page 375 Journey into Geometries by Marta Sved; Roads to Geometry by Edward C. Wallace and Stephen F. West / WILLIAM E. FENTON......Page 386 Polyominoes: A Guide to Puzzles and Problems in Tiling by George Martin / VICTOR G. FESER......Page 387 TELEGRAPHIC REVIEWS......Page 392 Number 5 / MAY 1993......Page 400 CONTENTS......Page 402 COMMENTS......Page 403 Thomas Archer Hirst-Mathematician Xtravagant I. A Yorkshire Surveyor / J. HELEN GARDNER and ROBIN J. WILSON......Page 404 Hyperbolic Geometry on a Hyperboloid / WILLIAM F. REYNOLDS......Page 411 A Simple Heuristic Proof of Hardy and Littlewood's Conjecture B / MICHAEL RUBINSTEIN......Page 425 The Pompeiu Problem / H. TURNER LAQUER......Page 430 A Quicker Convergence to Euler's Constant / DUANE W. DETEMPLE......Page 437 The Minimal Polynomial of COS(2\pi/n) / WILLIAM WATKINS and JOEL ZEITLIN......Page 440 The Equal Area Zones Property / B. RICHMOND and T. RICHMOND......Page 444 Graph Theory and the Game of Sprouts / MARK COPPER......Page 447 Elementary Proof of the Remez Inequality / Borislav Bojanov......Page 452 A Note on an Identity of Ramanujan / T. S. Nanjundiah......Page 454 On an Identity of Daubechies / Doron Zeilberger......Page 456 PICTURE PUZZLE......Page 457 THE AUTHORS......Page 458 LETTERS......Page 460 Data Compression / CATHERINE C. McGEOCH......Page 462 PROBLEMS AND SOLUTIONS......Page 467 Linear Algebra Through Geometry by Thomas Banchoff and John Wermer / JAMES KUZMANOVICH......Page 475 TELEGRAPHIC REVIEWS......Page 478 Number 6/ JUNE-JULY 1993......Page 486 CONTENTS......Page 488 COMMENTS......Page 489 Thomas Archer Hirst-Mathematician Xtravagent II. Student Days in Germany / J. HELEN GARDNER and ROBIN J. WILSON......Page 490 How to Make Wavelets / ROBERT S. STRICHARTZ......Page 498 A Matrix Maximum / WILLIAM C. WATERHOUSE......Page 516 Chaotic Motion of a Pendulum with Oscillatory Forcing / S. P. HASTINGS and J. B. MCLEOD......Page 522 An Application for the Curiosity (log_x N)' / DAVID A. WAGSTAFF, THEODORE A. NORMAN, and DOUGLAS M. CAMPBELL......Page 532 Vandermonde Strikes Again / MIRIAM SCHAPIRO GROSOF and GERALDINE TAIANI......Page 534 Embedding Countable Groups in 2-Generator Groups / Fred Galvin......Page 537 Abelian Forcing Sets / Joseph A. Gallian, Michael Reid......Page 539 PICTURE PUZZLE......Page 497 THE AUTHORS......Page 542 Is There a k-Anisohedral Tile for k > 5? / JOHN BERGLUND......Page 544 PROBLEMS AND SOLUTIONS......Page 548 Mathematics in Industrial Problems. Parts 1-4. Edited by Avner Friedman / ELLIS CUMBERBATCH......Page 556 TELEGRAPHIC REVIEWS......Page 559 Number 7 / AUGUST-SEPTEMBER 1993......Page 567 CONTENTS......Page 569 COMMENTS......Page 570 Thomas Archer Hirst-Mathematician Xtravagant III. Gottingen and Berlin / J. HELEN GARDNER and ROBIN J. WILSON......Page 571 Bisectors of Triangles and Tetrahedra / W. A. BEYER and BLAIR SWARTZ......Page 578 More on Rectangles Tiled by Rectangles / D. G. MEAD and S. K. STEIN......Page 593 Ramanujan-For Lowbrows I BRUCE C. BERNDT and S. BHARGA VA......Page 596 Chebychev Polynomials and Regular Polygons / D. Y. SAVIO and E. R. SURYANARAYAN......Page 609 Small-Group Learning / JULIAN WEISSGLASS......Page 614 A Fast Pick-Type Approximation for Areas of H-Polygons / DING REN, KRZYSZTOF KOODZIEJCZYK, GRATTAN MURPHY, and JOHN REAY......Page 621 PICTURE PUZZLE......Page 613 A Simple Example on Non-Sequentialness in Topological Spaces / Heinz Konig......Page 626 The Secant Method and the Golden Mean / Melvin J. Maron, Robert J. Lopez......Page 628 Rn Contains a Division Ring Does / Ayman Badawi......Page 631 A Further Simplification of Dixon's Proof of Cauchy's Integral Theorem / Peter A. Loeb......Page 632 Zero-Knowledge Proofs / CATHERINE C. McGEOCH......Page 634 THE AUTHORS......Page 638 PROBLEMS AND SOLUTIONS......Page 640 A First Course in Noncommutative Rings. By T.-Y. Lam / LANCE SMALL......Page 650 TELEGRAPHIC REVIEWS......Page 652 Number 8 / OCTOBER 1993......Page 660 CONTENTS......Page 662 COMMENTS......Page 663 Thomas Archer Hirst-Mathematician Xtravagant IV. Queenwood, France and Italy / J. HELEN GARDNER and ROBIN J. WILSON......Page 664 Thoughts on Innumeracy: Mathematics Versus the World? / PETER L. RENZ John Allen Paulos Replies......Page 673 Reflections on Rippling Water / MICHEL MENDES FRANCE......Page 684 The Principal Axis Theorem over Arbitrary Fields / DAVID MORNHINWEG, DANIEL B. SHAPIRO, and K. G. VALENTE......Page 690 The Fifty-Third William Lowell Mathematical Competition / LEONARD F. KLOSINSKI, GERALD L. ALEXANDERSON, and LOREN C. LARSON......Page 699 A Visual Explanation of Jensen's Inequality / TRISTAN NEEDHAM......Page 709 The Index of a Constrained Critical Point / CATHERINE HASSELL and ELMER REES......Page 713 On Some Irrational Decimal Fractions / NORBERT HEGYVARI......Page 720 PICTURE PUZZLE......Page 689 The Symmetry Principle for Mobius Transformations / Louis Brickman......Page 722 A Short Proof for Romberg Integration / T. von Petersdorff......Page 724 An Elementary Proof that the Borromean Rings are Non-Splittable / Ollie Nanyes......Page 727 LETTER TO THE EDITOR......Page 730 Open Problems in Pattern Avoidance / JAMES CURRIE......Page 731 THE AUTHORS......Page 735 PROBLEMS AND SOLUTIONS......Page 737 Ordinary Differential Equations. By Vladimir I. Arnol'd / FRED BRAUER......Page 751 TELEGRAPHIC REVIEWS......Page 753 Number 9 / NOVEMBER 1993......Page 759 CONTENTS......Page 761 COMMENTS......Page 762 Thomas Archer Hirst-Mathematician Xtravagant V. London in the 1860s / J. HELEN GARDNER and ROBIN J. WILSON......Page 763 From the Post-Markov Theorem Through Decision Problems to Public-Key Cryptography / IRIS LEE ANSHEL and MICHAEL ANSHEL......Page 771 Famous Nonmathematicians / STEVEN G. BUYSKE......Page 781 The Fundamental Theorem of Linear Algebra / GILBERT STRANG......Page 784 A Simple Proof of the Jordan-Alexander Complement Theorem / ALBRECHT DOLD......Page 792 Squaring the Circle with Holes / HANSKLAUS RUMMLER......Page 794 PICTURE PUZZLE......Page 783 Simplifying the Proof of Dirichlet's Theorem / Paul Monsky......Page 797 Why is P2 Not Embeddable in R3? / Hiroshi Maehara......Page 798 Polynomial Root Dragging / Bruce Anderson......Page 800 Parallel Addition / CATHERINE C. MCGEOCH......Page 804 THE AUTHORS......Page 808 PROBLEMS AND SOLUTIONS......Page 811 Second Year Calculus: From Celestial Mechanics to Special Relativity. By David M. Bressoud / WILLIAM FARIS......Page 820 TELEGRAPHIC REVIEWS......Page 825 Number 10 / DECEMBER 1993......Page 831 CONTENTS......Page 833 COMMENTS......Page 834 Thomas Archer Hirst-Mathematician Xtravagant VI. Years of Decline / J. HELEN GARDNER and ROBIN J. WILSON......Page 835 Densest Pac kings of Congruent Circles in an Equilateral Triangle / HANS (J. B. M.) MELISSEN......Page 844 Partnerships / ALAN H. SCHOENFELD......Page 854 A Simple Proof of Pascal's Hexagon Theorem / JAN VAN YZEREN......Page 858 The Mathematical Relationship between Kepler's Laws and Newton's Laws / Andrew T. Hyman......Page 860 A Short Proof of a Result on Polynomials / Razvan Gelca......Page 864 Two Amusing Dynkin Diagram Graph Classifications / Robert A. Proctor......Page 865 POSTCARDS FROM MAX / PAUL HALMOS......Page 870 A Quarter Century of Monthly Unsolved Problems, 1969-1993 / RICHARD K. GUY......Page 873 THE AUTHORS......Page 878 PROBLEMS AND SOLUTIONS......Page 879 A First Course in Chaotic Dynamical Systems: Theory and Experiment. By Robert Devaney. A First Course in Chaotic Dynamical Systems: Labs 1-6. By James Georges, Del Johnson and Robert Devaney / PHILIP D. STRAFFIN......Page 889 TELEGRAPHIC REVIEWS......Page 892 INDEX TO VOLUME 100......Page 898