Single Digits - by Marc Chamberland (Paperback)

Book Synopsis

The remarkable properties of the numbers one through nine

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.

From the Back Cover

"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

Review Quotes

"[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"

"Boring deep into the innocuous-looking number one, Chamberland opens an unexpected entry point into a dizzying maze of infinities. . . . A bracing mathematical adventure."-- "Booklist"

"Chamberland makes this an entertaining and historical exposition, using wit and humor throughout."-- "Math Horizons"

"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. . . . 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."---DVD, Lunar and Planetary Information Bulletin

"Everyone will find something interesting for themselves and the book is ideal for math circles and for students who are to be indefinitely hooked to mathematics."---Radoslav M Dimitric, Zentralblatt Math

"Fascinating. . . . Chamberland offers enticing explanations that will leave readers hungry to know more. This wonderful book never loses its focus or momentum."-- "Publishers Weekly"

"For instructors of math courses of all levels, the vignettes in Single Digits can provide a very readable introduction or jumping-off point for discussions and projects. . . . In an introductory group theory course, it would be a good exercise for students to consider perfect riffle shuffles in decks of size other than 52. Finally, a statistics class collecting and analyzing real-world data sets could consider whether Benford's Law applies in their situation."---Matthew Welz, MAA Focus

"I highly recommend Single Digits: In Praise of Small Numbers. It would be a fine addition to any high school or math department library. As a carefully curated set of interesting topics, it would serve as a good place to start exploring the ocean of ideas in mathematics."---Bruce Cohen, NCTM

"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

"The exotics like pi and e have gotten their share of attention in the world of popular mathematical writing. Now it's time to give proper attention to the integers 1 through 9. . . . [Single Digits] is consistently entertaining and well-written."-- "MAA Reviews"

"The range of topics included virtually guarantees that any reader will find new and unfamiliar material to enjoy. . . . [Single Digits] is a very enjoyable book which, at many points, makes some very deep mathematics quite accessible. Highly recommended."---Keith Johnson, CMS Notes

"To put it simply, this book is a delight. Chamberland has assembled a fascinating collection of vignettes, each tied to a digit from one to nine, that inform, entertain, and intrigue. . . . This wide spectrum of ideas is consistently interesting, and the author's skill in mining each nugget is worthy of great respect."-- "Choice"

About the Author

Marc Chamberland is professor of mathematics and natural sciences at Grinnell College. He is the creator of the YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone.