Number 1 / JANUARY 1994......Page 1
CONTENTS......Page 3
COMMENTS......Page 4
Introduction to Fermat's Last Theorem / DAVID COX......Page 5
Future Elementary Teachers: The Neglected Constituency / THOMAS W. HUNGERFORD......Page 17
Galois Theory for Beginners / JOHN STILLWELL......Page 24
Into the Hourglass: Reflections on the Forces Acting on a Granular Material/ E. BRUCE PITMAN......Page 30
Orderly Currencies / JOHN DEWEY JONES......Page 38
An Interior Fixed Point Property of the Disc / ROBERT F. BROWN and ROBERT E. GREENE......Page 41
Le Cam's Inequality and Poisson Approximations / J. MICHAEL STEELE......Page 50
PICTURE PUZZLE......Page 29
A Generalization of a Theorem of Euler / DORINA MITREA AND MARIUS MITREA......Page 57
The Existence of a Triangle with Prescribed Angle Bisector Lengths / PETRU MIRONESCU and LAURENTIU PANAITOPOL......Page 60
Turing Machines and Computational Complexity / BILL MARION......Page 63
The Evolution of Integration / A. SHENITZER and J. STEPRANS......Page 68
THE AUTHORS......Page 75
PROBLEMS AND SOLUTIONS......Page 77
Mathematical Cranks, by Underwood Dudley / IAN STEWART......Page 89
Complex Analysis: The Geometric Viewpoint, by Steven G. Krantz / JOHN POLKING......Page 93
TELEGRAPHIC REVIEWS......Page 97
Number 2 / FEBRUARY 1994......Page 109
CONTENTS......Page 111
COMMENTS......Page 112
Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to J. Sutherland Frame / DAVID W. BALLEW......Page 113
A New Look at Euler's Theorem for Polyhedra / BRANKO GRUNBAUM and G. C. SHEPHARD......Page 115
Otto Neugebauer: Reminiscences and Appreciation / PHILIP J. DAVIS......Page 135
From the Buffon Needle Problem to the Kreiss Matrix Theorem / ELIAS WEGERT and LLOYD N. TREFETHEN......Page 138
A Counterexample for Germain /WILLIAM C. WATERHOUSE......Page 146
Cubic Equations, or Where Did the Examination Question Come From? / H. B. GRIFFITHS and A. E. HIRST......Page 157
PICTURE PUZZLE......Page 145
On the Identity of Polyhedra / HELLMUTH STACHEL......Page 168
More on the Pompeiu Problem / DAVID C. ULLRICH......Page 171
Every Number Is Expressible as the Sum of How Many Polygonal Numbers? / RICHARD K. GUY......Page 175
THE AUTHORS......Page 179
PROBLEMS AND SOLUTIONS......Page 181
Reality Rules 1. The Fundamentals; 11. The Frontier. By John Casti / RUTHERFORD ARIS......Page 192
Geometry of Surfaces. By John Stillwell / DAVID L. WEBB......Page 194
TELEGRAPHIC REVIEWS......Page 197
Number 3 / MARCH 1994......Page 209
CONTENTS......Page 211
COMMENTS......Page 212
A Marvelous Proof / FERNANDO Q. GOUVEA......Page 213
Triangulating the Circle, at Random / DAVID ALDOUS......Page 233
Hypatia and Her Mathematics / MICHAEL A. B. DEAKIN......Page 244
Calculus II and Euler Also (with a Nod to Series Integral Remainder Bounds) / RICHARD BARSHINGER......Page 254
A Focusing Property of the Ellipse / MARC FRANTZ......Page 260
Reflections Can Be Trapped / ROBERTO PEIRONE......Page 269
Euler's Theorem / KATHERINE HEINRICH and PETER HORAK......Page 270
PICTURE PUZZLE......Page 271
Universal Traversal Sequences / JOAN FEIGENBAUM and NICK REINGOLD......Page 272
What Are Algebraic Integers and What Are They For? / JOHN STILLWELL......Page 276
THE AUTHORS......Page 281
PROBLEMS AND SOLUTIONS......Page 283
Revolutions in Mathematics. Edited by Donald Gillies / MICHAEL MAHONEY......Page 293
TELEGRAPHIC REVIEWS......Page 298
Number 4 / APRIL 1994......Page 317
CONTENTS......Page 319
COMMENTS......Page 320
Pizza Slicing, Phi's and the Riemann Hypothesis / EDWARD A. BENDER, OREN PATASHNIK, and HOWARD RUMSEY, JR.......Page 321
Rational Periodic Points of the Quadratic Function Qc(x) = x 2 + c / RALPH WALDE and PAULA RUSSO......Page 332
Frechet vs. Caratheodory / ERNESTO ACOSTA G. and CESAR DELGADO G.......Page 346
Odd Magic Powers / A. C. THOMPSON......Page 353
Mathematicians, Including Undergraduates, Look at Soap Bubbles / FRANK MORGAN......Page 357
A Proof of Dilworth's Chain Decomposition Theorem / FRED GALVIN......Page 366
On Intervals, Transitivity = Chaos / MICHEL VELLEKOOP and RAOUL BERGLUND......Page 367
Proof of a Mixed Arithmetic-Mean, Geometric-Mean Inequality / KIRAN KEDLAYA......Page 369
ApSimon's Mints Problem......Page 372
THE AUTHORS......Page 374
PROBLEMS AND SOLUTIONS......Page 376
Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, edited by A. N. Kolmogorov and A. P. Yushkevich / KAREN HUNGER PARSHALL......Page 383
Calculus Gems: Brief Lives and Memorable Mathematics. By George F. Simmons / DAVID J. PENGELLEY......Page 388
TELEGRAPHIC REVIEWS......Page 395
Number 5 / MAY 1994......Page 417
CONTENTS......Page 419
COMMENTS......Page 420
On the Geometry of Piecewise Circular Curves / THOMAS BANCHOFF and PETER GIBLIN......Page 421
The Two Envelope Paradox / ELLIOT LINZER......Page 435
Fourier Series of Polygons / ALAIN ROBERT......Page 438
The Paradox of Nontransitive Dice / RICHARD P. SAVAGE, JR.......Page 447
Squares Expressible as Sum of Consecutive Squares / LAURENT BEECKMANS......Page 455
Square Roots mod p / STEPHEN M. TURNER......Page 461
Kummer's Test Gives Characterizations for Convergence or Divergence of all Positive Series / JINGCHENG TONG......Page 468
Isometries of \ell_p-norm / CHI-KWONG LI and WASIN SO......Page 470
A Trace Inequality for Unitary Matrices / BOYING WANG and FUZHEN ZHANG......Page 471
An Elementary Proof of the Square Summability of the Discrete Hilbert Transform / LOUKAS GRAFAKOS......Page 474
Does Anybody Really Know What Time It Is? / CATHERINE C. McGEOCH......Page 477
How Hyperbolic Geometry Became Respectable / ABE SHENITZER......Page 482
THE AUTHORS......Page 489
PROBLEMS AND SOLUTIONS......Page 491
The Lure of the Integers. By Joe Roberts / PAUL T. BATEMAN and HAROLD G. DIAMOND......Page 498
Excursions in Calculus: An Interplay of the Continuous and the Discrete. By Robert M. Young / ANITA E. SOLOW......Page 500
TELEGRAPHIC REVIEWS......Page 503
Number 6 / JUNE-JULY 1994......Page 525
CONTENTS......Page 527
COMMENTS......Page 528
Juggling Drops and Descents / JOE BUHLER, DAVID EISENBUD, RON GRAHAM, and COLIN WRIGHT......Page 529
Teaching Integration by Substitution / DAVID GALE......Page 542
Workable Gears, Archimedian Solids and Planar Bipartite Graphs / GARY GORDON......Page 549
On the Kummer Solutions of the Hypergeometric Equation / REESE T. PROSSER......Page 557
Reflections on a Mira / JOHN W. EMERT, KAY I. MEEKS, and ROGER B. NELSON......Page 566
Buffon Noodles / ED WAYMIRE......Page 572
PICTURE PUZZLE......Page 581
On a Curious Property of Counting Sequences / VICTOR BRONSTEIN and A VIEZRI S. FRAENKEL......Page 582
Chaos Without Nonperiodicity / CARSTEN KNUDSEN......Page 585
A Reverse Stolarsky's Inequality / JOSIP PECARIC......Page 587
A Note on Some Irrational Decimal Fractions / A. MCD. MERCER......Page 589
THE AUTHORS......Page 591
A Possible Permanent Formula / DAVID CALLAN......Page 593
PROBLEMS AND SOLUTIONS......Page 596
Ideals, Varieties, and Algorithms. By David Cox, John Little, and Donal O'Shea / MOSS SWEEDLER......Page 604
TELEGRAPHIC REVIEWS......Page 609
Number 7 / AUGUST-SEPTEMBER 1994......Page 625
CONTENTS......Page 627
COMMENTS......Page 628
A Tale of Two CD's / DAN KENNEDY......Page 629
Three Problems in Search of a Measure / JONATHAN L. KING......Page 635
The n-Queens Problem / IGOR RIVIN, ILAN VARDI, and PAUL ZIMMERMANN......Page 655
What's the Difference Between Cantor Sets? / ROGER L. KRAFT......Page 666
Morphisms, Squarefree Strings, and the Tower of Hanoi Puzzle / JEAN-PAUL ALLOUCHE, DAN ASTOORIAN, JIM RANDALL, and JEFFREY SHALLIT......Page 677
Sierpinski's Theorem Is Deducible from Euler and Dirichlet / A. A. AGEEV......Page 685
On Nonnegativity of Symmetric Polynomials / F. MATUS......Page 687
New Tricks for Old Trees: Maps and the Pigeonhole Principle / N. GRAHAM, R. C. ENTRINGER, AND L. A. SZEKELY......Page 690
Do You Know the Way to Vertex A? / JEFF ONDICH......Page 694
On the Calculus of Variations and Its Major Influences on the Mathematics of the First Half of Our Century. Part I / ERWIN EREYSZIG......Page 700
THE AUTHORS......Page 705
PROBLEMS AND SOLUTIONS......Page 707
How to Teach Mathematics, By Steven G. Krantz / MEYER JERISON......Page 718
TELEGRAPHIC REVIEWS......Page 721
Number 8 / OCTOBER 1994......Page 741
CONTENTS......Page 743
COMMENTS......Page 744
Behind the Scenes of a Random Dot Stereogram / MARIA S. TERRELL and ROBERT E. TERRELL......Page 745
The Fifty-Fourth William Lowell Putnam Mathematical Competition / LEONARD F. KLOSINSKI, GERALD L. ALEXANDERSON, and LOREN C. LARSON......Page 755
Literacy in the Language of Mathematics / JAMES O. BULLOCK......Page 765
Fractional and Trigonometric Expressions for Matrices / GORO SHIMURA......Page 774
Noether Lasker Primary Decomposition Revisited / BARBARA L. OSOFSKY......Page 789
Elementary Infinite Sources of Non-Unique Factorization Rings / S. STEIN and S. SZABO......Page 799
Apropos Two Notes on Notation / ANTAL E. FEKETE......Page 801
The Coin Exchange Problem for Arithmetic Progressions / AMITABHA TRIPATHI......Page 809
Congruence of Triangles / LEONARD GILLMAN......Page 812
A Short Elementary Proof of the Mohr-Mascheroni Theorem / NORBERT HUNGERBUHLER......Page 814
Which Triangles Are Plane Sections of Regular Tetrahedra? / FOLKE ERIKSSON......Page 818
THE AUTHORS......Page 820
PROBLEMS AND SOLUTIONS......Page 822
Brouwer's Intuitionism. By Walter P. van Stigt / C. SMORYNSKI......Page 829
TELEGRAPHIC REVIEWS......Page 833
RESPONSE TO COMMENT On PAGE 714......Page 839
Number 9 / NOVEMBER 1994......Page 849
CONTENTS......Page 851
COMMENTS......Page 852
Georg Cantor and Transcendental Numbers / ROBERT GRAY......Page 853
The SOOth Anniversary of the Sharing Problem (The Oldest Problem in the Theory of Probability) / MILTON SOBEL and KRZYSZTOF FRANKOWSKI......Page 867
What Is Teaching?/ PAUL R. HALMOS......Page 882
What Is Wrong with the Definition of dy / dx? / HUGH THURSTON......Page 889
A Stochastic Approach to the Gamma Function / LOUIS GORDON......Page 892
Arrangements and Topological Planes / JACOB E. GOODMAN, RICHARD POLLACK, RAPHAEL WENGER, and TUDOR ZAMFIRESCU......Page 900
An Application of Fourier Series to the Most Significant Digit Problem / JEFF BOYLE......Page 913
Cross Product Identities in Arbitrary Dimension / ANDREW DITTMER......Page 921
A Non-Constant, Continuous Function on the Plane Whose Integral on Every Line Is Zero / D. H. ARMITAGE......Page 926
Chu's 1303 Identity Implies Bombieri's 1990 Norm-Inequality (Via an Identity of Beauzamy and Degot) / DO RON ZEILBERGER......Page 928
How to Stay Competitive / CATHERINE C. McGEOCH......Page 931
On the Calculus of Variations and Its Major Influences on the Mathematics of the First Half of Our Century. Part II / ERWIN KREYSZIG......Page 936
THE AUTHORS......Page 943
PROBLEMS AND SOLUTIONS......Page 945
Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. By Lam Lay Yong and Ang Tian Se / FRANK SWETZ......Page 955
TELEGRAPHIC REVIEWS......Page 958
Number 10 / DECEMBER 1994......Page 973
CONTENTS......Page 975
COMMENTS......Page 976
The Rectilinear Crossing Number of a Complete Graph and Sylvester's "Four Point Problem" of Geometric Probability / EDWARD R. SCHEINERMAN and HERBERT S. WILF......Page 977
String Matching for the Novice / ORA E. PERCUS and JEROME K. PERCUS......Page 982
Bernoulli Trials and Number Theory / DON RAWLINGS......Page 986
What Is the Shape of a Mylar Balloon? / WILLIAM H. PAULSEN......Page 991
Euler's Theorem for Polyhedra: A Topologist and Geometer Respond / PETER HILTON and JEAN PEDERSEN......Page 997
The Role of Paradoxes in the Evolution of Mathematics / I. KLEINER and N. MOVSHOVITZ-HADAR......Page 1001
Regions in the Complex Plane Containing the Eigenvalues of a Matrix / RICHARD A. BRUALDI and STEPHEN MELLENDORF......Page 1013
Characterization of Solvable Quintics x^5 + ax + b / BLAIR K. SPEARMAN and KENNETH S. WILLIAMS......Page 1024
A Halmos Problem and a Related Problem / JOHN B. COSGRAVE......Page 1031
A "Popular" Class Number Formula / KURT GIRSTMAIR......Page 1035
Variations on Wolstenholme's Theorem / EMRE ALKAN......Page 1039
The Second-Partials Test for Local Extrema of f(x, y) / LEONARD GILLMAN......Page 1042
Mousetrap / RICHARD K. GUY and RICHARD J. NOWAKOWSKI......Page 1045
THE AUTHORS......Page 1049
PROBLEMS AND SOLUTIONS......Page 1051
Linear Programs and Related Problems, by Evar D. Nering and Albert W. Tucker / STEPHEN B. MAURER......Page 1060
TELEGRAPHIC REVIEWS......Page 1065
INDEX TO VOLUME 101......Page 1071

lgrsnf/_491082.c67d9de855f15d70140d6ae0b50a5f34.djvu

nexusstc/c67d9de855f15d70140d6ae0b50a5f34.djvu

Google

United States, United States of America

2011 12 30

lg771943

{"last_page":1088,"periodical":"American Mathematical Monthly, Volume 101, No. 1-10, 1994","publisher":"Mathematical Association of America"}

2012-02-04