Synopses & Reviews
"A veritable potpourri of mathematical factoids,
Single Digits will provide you with conversational ammunition for all manner of nerdy gatherings."
--Henry Reich, creator of MinutePhysics and MinuteEarth"Dispensing incisive, brief expositions of mathematical observations, facts, theorems, proofs, conjectures, and open problems, this cornucopia of a book ranges through geometry, number theory, combinatorics, topology, and many other areas. From the elegantly elementary to the sublimely difficult, each of its short sections is liable to stimulate an eager search for further enlightenment, whether from the internet, the library, or your own mind."--Avner Ash, coauthor of Elliptic Tales
"A survey of mathematical gems, ancient and modern, this book is certain to arouse the curiosity of anyone with even a passing interest in mathematics. Chamberland's clear explanations provide an enticing introduction to each topic and will make you want to learn more."--Jamie Pommersheim, coauthor of Number Theory
"This book describes properties associated with the numbers one to nine and connects important areas of mathematics, including number theory, geometry, chaos theory, and applied mathematics. Single Digits is filled with nuggets of mathematical information, compelling topics, and interesting ideas for anyone curious about the subject."--Lee Fothergill, Mount Saint Mary College
"A celebration of small numbers, Single Digits presents mathematical vignettes organized by their connection to single nonzero digits. Progressing from the elementary to the more elaborate, Chamberland brings together some really interesting mathematics, and his well-told stories will intrigue a general, knowledgeable audience."--Jennifer Quinn, University of Washington, Tacoma
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"[B]oth amateur and professional mathematicians alike will find new items of interest here. . . . [A] welcome, splendid, fruitful addition to my math bookshelf."--Math Tango blog
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"The collection is outright delightful. It will agitate the minds of students and shake the sense of know-all off many a professional and most of the amateurs."--Alexander Bogomolny, Cut the Knot blog
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"Chamberland . . . produces a fascinating, compact set of entries on mathematical problems, conjectures, and theorems. This wonderful book never loses its focus or momentum."--Publishers Weekly, starred review
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"A bracing mathematical adventure."--Booklist
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"[C]onsistently entertaining and well-written. . . . [Single Digits] would be an ideal gift for a high school student who might have an interest in mathematics. It's also fun just to pick up and browse."-- William J. Satzer, MAA Reviews
Synopsis
In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really -six degrees of separation- between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, the number of guards needed to protect an art gallery, problematic election results and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.
Synopsis
The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In
Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.
Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan's conjecture, and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem.
Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.
About the Author
Marc Chamberland is the Myra Steele Professor of Natural Science and Mathematics at Grinnell College. He is the creator of the YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone.