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The Best Writing on Mathematics


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Table of Contents

Introduction - Mircea Pitici xi A Dusty Discipline - Michael J. Barany and Donald MacKenzie 1 How Puzzles Made Us Human - Pradeep Mutalik 7 Let the Games Continue - Colm Mulcahy and Dana Richards 14 Challenging Magic Squares for Magicians - Arthur T. Benjamin and Ethan J. Brown 26 Candy Crush's Puzzling Mathematics - Toby Walsh 38 Chaos on the Billiard Table - Marianne Freiberger 47 Juggling with Numbers - Erik R. Tou 63 The Quest for Randomness - Scott Aaronson 69 Synthetic Biology, Real Mathematics - Dana Mackenzie 93 At the Far Ends of a New Universal Law - Natalie Wolchover 99 Twisted Math and Beautiful Geometry - Eli Maor and Eugen Jost 107 Kenichi Miura's Water Wheel, or The Dance of the Shapes of Constant Width - Burkard Polster 119 Durer: Disguise, Distance, Disagreements, and Diagonals! - Annalisa Crannell, Marc Frantz, and Fumiko Futamura 132 The Quaternion Group as a Symmetry Group - Vi Hart and Henry Segerman 141 The Steiner-Lehmus Angle-Bisector Theorem - John Conway and Alex Ryba 154 Key Ideas and Memorability in Proof - Gila Hanna and John Mason 167 The Future of High School Mathematics - Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer, Alan Schoenfeld, Cathy Seeley, Dan Teague, and Zalman Usiskin 181 Demystifying the Math Myth: Analyzing the Contributing Factors for the Achievement Gap between Chinese and U.S. Students - Guili Zhang and Miguel A. Padilla 187 The Pigeonhole Principle, Two Centuries before Dirichlet - Benoit Rittaud and Albrecht Heeffer 201 A Prehistory of Nim - Lisa Rougetet 207 Godel, Gentzen, Goodstein: The Magic Sound of a G-String - Jan von Plato 215 Global and Local - James Franklin 228 Mathematical Beauty, Understanding, and Discovery - Carlo Cellucci 241 A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics - Mark Balaguer 265 Writing about Math for the Perplexed and the Traumatized - Steven Strogatz 280 Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications - Domenico Napoletani, Marco Panza, and Daniele C. Struppa 293 The Statistical Crisis in Science - Andrew Gelman and Eric Loken 305 Color illustration section follows page 316 Statistics and the Ontario Lottery Retailer Scandal - Jeffrey S. Rosenthal 319 Never Say Never - David J. Hand 332 Contributors 337 Notable Writings 349 Acknowledgments 359 Credits 361

About the Author

Mircea Pitici holds a PhD in mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.


"The Best Writing on Mathematics does not shy away from mathematics, and that is why it shines. Pitici has done a wonderful job curating articles that form a cohesive ... volume for readers seeking more than what popular mathematics books have to offer. Overall, this is a great book for the mathematically-experienced reader seeking to connect to mathematics outside of the world of textbooks and tests."--Douglas Whitaker, Key Reporter "[A]nother wonderful variety of mathematical writings, this time with a distinct focus on mathematical games and puzzles. These intriguing--and sometimes unsolved--puzzles provide fuel for much contemplation and exploration of varied topics such as billiards, juggling, and the game Candy Crush... Those picking up this collection for the math itself should be pleasantly surprised by the enlightening interdisciplinary work in philosophy, history, and art."--Publishers Weekly "Pitici offers his annual selection of intriguing mathematical articles, and happily, 2015 was a banner year. [An] eclectic collection of nontechnical papers understandable to any reader... A well-chosen collection supplemented by an outstanding further reading list."--Harold D. Shane, Library Journal[ "I like expository articles on mathematics, but seldom have the time during the academic year to seek them out, so it is always a pleasure to have somebody like Pitici assemble a collection of good ones for me. This year's assortment, like those of the last few years, did not disappoint."--Mark Hunacek, MAA Reviews "Dealing with topics of general interest--as history and philosophy, teaching, the occurrence of mathematics in everyday life, etc.--presented in an attractive and accessible manner, the books appeals to a large audience, including mathematicians of all levels of instruction, but also to anyone interested in the development of science and its applications."--Horia F. Pop, Studia Mathematica "The idea behind this great series, which Pitici describes as 'accessible but nontrivial content that presents for mathematicians and for the general public a wide assortment of informed and insightful perspectives on pure and applied mathematics, on topics related to the learning and teaching of mathematics, on the practice and practicality of mathematics, on the social and institutional aspects in which the mathematics themes, or on other themes related to mathematics,' was clearly presented in last year's book and successfully continued in the one in front of us. We trust and hope that this will carry on in future years and we are definitely looking forward to it."--Aleksandar M. Nikoli?, MathSciNet "I found this book to be a great resource. The articles are easy to read and interesting to ponder. This book will be a valuable resource when my students in algebra and geometry want to look at a math concept for a project. The recent math applications in this book are a valuable resource."--Matthew Tucker, National Council of Teachers of Mathematics

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