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Single Digits : In Praise of Small Numbers
by Marc Chamberland


Overview -

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?  Read more...


 
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    Single Digits (Paperback)
    Published: 2017-06-06
    Publisher: Princeton University Press
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More About Single Digits by Marc Chamberland
 
 
 
Overview

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.


 
Details
  • ISBN-13: 9780691161143
  • ISBN-10: 0691161143
  • Publisher: Princeton University Press
  • Publish Date: June 2015
  • Page Count: 240


Related Categories

Books > Mathematics > Number Theory
Books > Mathematics > Number Systems
Books > Mathematics > Numerical Analysis

 
Publishers Weekly Reviews

Publishers Weekly® Reviews

  • Reviewed in: Publishers Weekly, page .
  • Review Date: 2015-04-27
  • Reviewer: Staff

Chamberland, professor of mathematics at Grinnell College, produces a fascinating, compact set of entries on mathematical problems, conjectures, and theorems. The theme of single digits provides a novel framework for all the mathematics, tying together disparate theorems in sections related to a single number. Each brief entry is clearly explained, making the problems comprehensible and accessible to math lovers of all backgrounds, though they do vary in difficulty and complexity. Chamberland addresses a wide array of elegant mathematical concepts that are generally foreign or obscure to the lay public, including the Stern sequence, Thue-Morse sequences, and Marden’s Theorem. More serious math lovers may want to supplement the introductions given in the book with further research, not because of any lack of critical information, but because Chamberland offers enticing explanations that will leave readers hungry to know more. Epigraphs at each chapter’s beginning include quotes from the Buddha, W.E.B. Du Bois, Alexandre Dumas, and Paul McCartney, among others, informally connecting the material to human culture. Chamberland also presents a few problems for readers to solve on their own, with answers provided in the last chapter. This wonderful book never loses its focus or momentum, and readers may dip into it for a few entries or read straight through. (June)

 
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