Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi

Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi

Author: Martin Gardner

Publisher:

Published: 2008-09-08

Total Pages: 222

ISBN-13:

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This book of the earliest of Gardner's enormously popular Scientific American columns and puzzles continues to challenge and fascinate readers. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.


Hexaflexagons and Other Mathematical Diversions

Hexaflexagons and Other Mathematical Diversions

Author: Martin Gardner

Publisher: American Mathematical Soc.

Published: 2020-10-05

Total Pages: 211

ISBN-13: 1470463520

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Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.


Mathematical Carnival

Mathematical Carnival

Author: Martin Gardner

Publisher: American Mathematical Soc.

Published: 2020-10-06

Total Pages: 311

ISBN-13: 1470463571

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Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, first published in 1975, contains columns published in the magazine from 1965-1967. This 1989 MAA edition contains a foreword by John H. Conway and a postscript and extended bibliography added by Gardner for this edition.


Arithmetical Wonderland

Arithmetical Wonderland

Author: Andy Liu

Publisher: American Mathematical Soc.

Published: 2015-12-31

Total Pages: 241

ISBN-13: 0883857898

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Arithmetical Wonderland is intended as an unorthodox mathematics textbook for students in elementary education, in a contents course offered by a mathematics department. The scope is deliberately restricted to cover only arithmetic, even though geometric elements are introduced whenever warranted. For example, what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid is showcased. Many students find mathematics somewhat daunting. It is the [Author];'s belief that much of that is caused not by the subject itself, but by the language of mathematics. In this book, much of the discussion is in dialogues between Alice, of Wonderland fame, and the twins Tweedledum and Tweedledee who hailed from Through the Looking Glass. The boys are learning High Arithmetic or Elementary Number Theory from Alice, and the reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language. Nevertheless, the book has considerable depth. It examines many arcane corners of the subject, and raises rather unorthodox questions. For instance, Alice tells the twins that six divided by three is two only because of an implicit assumption that division is supposed to be fair, whereas fairness does not come into addition, subtraction or multiplication. Some topics often not covered are introduced rather early, such as the concepts of divisibility and congruence.


The Mathematics of Various Entertaining Subjects

The Mathematics of Various Entertaining Subjects

Author: Jennifer Beineke

Publisher: Princeton University Press

Published: 2017-09-05

Total Pages: 408

ISBN-13: 0691171920

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The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic’s background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.


Alice in Space

Alice in Space

Author: Gillian Beer

Publisher: University of Chicago Press

Published: 2018-01-26

Total Pages: 307

ISBN-13: 022656469X

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An examination of Carroll's books about Alice explores the contextual knowledge of the time period in which it was written, addressing such topics as time, games, mathematics, and taxonomies.


Classical Geometry

Classical Geometry

Author: I. E. Leonard

Publisher: John Wiley & Sons

Published: 2014-04-14

Total Pages: 501

ISBN-13: 1118679199

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Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes: Multiple entertaining and elegant geometry problems at the end of each section for every level of study Fully worked examples with exercises to facilitate comprehension and retention Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications An approach that prepares readers for the art of logical reasoning, modeling, and proofs The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.


The Whys of a Philosophical Scrivener

The Whys of a Philosophical Scrivener

Author: Martin Gardner

Publisher: St. Martin's Griffin

Published: 1999-08-21

Total Pages: 494

ISBN-13: 1466823321

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The Whys of a Philosophical Scrivener showcases Martin Gardner as the consummate philosopher, thinker, and great mathematician that he is. Exploring issues that range from faith to prayer to evil to immortality, and far beyond, Garnder challenges the discerning reader with fundamental questions of classical philosophy and life's greater meanings. Recalling such philosophers was Wittgenstein and Arendt, The Whys of Philosophical Scrivener embodies Martin Garner's unceasing interest and joy in the impenetrable mysteries of life.


Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers

Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers

Author: Thane Plambeck

Publisher: American Mathematical Soc.

Published: 2020-03-06

Total Pages: 236

ISBN-13: 147044870X

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The Gathering 4 Gardner is a biannual conference founded—and for many years organized—by Tom Rodgers to celebrate the spirit of Martin Gardner. While primarily concerned with recreational mathematics, most of Gardner's intellectual interests are featured, including magic, literature, philosophy, puzzles, art, and rationality. Gardner's writing inspired several generations of mathematicians by introducing us to the joy of discovery and exploration, and the Gathering's aim is to continue that tradition of inspiration. This volume, a tribute to Rodgers and Gardner, consists of papers originally presented at the Gathering 4 Gardner meetings. Recreational mathematics is strongly prominent with contributions from Neil Sloane, Richard Guy, Solomon Golomb, Barry Cipra, Erik Demaine, and many others. There are games and puzzles, including new Nim-like games, chess puzzles, coin weighings, coin flippings, and contributions that combine art and puzzles or magic and puzzles. Two historical articles present the stories of combinatorial game theory and the search for God's number for Rubik's Cube. Anyone who finds pleasure in clever and intriguing intellectual puzzles will find much to enjoy in Barrycades and Septoku.