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.
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. "Fascinating. . . . Chamberland offers enticing explanations that will leave readers hungry to know more. This wonderful book never loses its focus or momentum." "[B]oth amateur and professional mathematicians alike will find new items of interest here. . . . [A] welcome, splendid, fruitful addition to my math bookshelf." "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 "Boring deep into the innocuous-looking number one, Chamberland opens an unexpected entry point into a dizzying maze of infinities. . . . A bracing mathematical adventure." "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." "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." "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." "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 "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 appli
