Single Digits: In Praise of Small Numbers

By Marc Chamberland

The numbers one via 9 have awesome mathematical homes and features. for example, why do 8 ideal card shuffles go away a typical deck of playing cards unchanged? Are there particularly "six levels of separation" among all pairs of individuals? and the way can any map want merely 4 shades to make sure that no areas of an identical colour contact? In Single Digits, Marc Chamberland takes readers on a desirable exploration of small numbers, from one to 9, taking a look at their heritage, functions, and connections to varied components of arithmetic, together with quantity thought, geometry, chaos idea, numerical research, and mathematical physics.

Each bankruptcy specializes in a unmarried digit, starting with effortless strategies that turn into extra complicated because the bankruptcy progresses. Chamberland covers huge numerical territory, reminiscent of illustrating the ways in which the quantity 3 connects to chaos idea, an unsolved challenge regarding Egyptian fractions, the variety of guards had to shield an paintings gallery, and tricky election effects. He considers the position of the quantity seven in matrix multiplication, the Transylvania lottery, synchronizing signs, and listening to the form of a drum. all through, he introduces readers to an array of puzzles, reminiscent of excellent squares, the 4 hats challenge, Strassen multiplication, Catalan's conjecture, and a lot more. The book's brief sections may be learn independently and digested in bite-sized chunks--especially sturdy for studying in regards to the Ham Sandwich Theorem and the Pizza Theorem.

Appealing to highschool and faculty scholars, specialist mathematicians, and people mesmerized via styles, this publication exhibits that unmarried digits supply a plethora of probabilities that readers can count number on.

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