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.
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.
"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
"[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
"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
"A bracing mathematical adventure."--Booklist
"[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
"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
"Chamberland makes this an entertaining and historical exposition, using wit and humor throughout. . . . Single Digits has made me appreciate the many connections between the digits one to nine and diverse areas of mathematics."--Heather Moon, Math Horizons