John Horton Conway

In The Book of Numbers, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. The Book of Numbers features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim," the authors write, "is to bring to the inquisitive reader...an explanation of the many ways the word 'number' is used." They explore patterns that emerge in arithmetic, algebra, and geometry, describe these patterns' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematicians and writers could do.

The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.

"By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies."--Cover.

Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 2nd edition, volume 4.

Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 2nd edition, volume 3.

Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 2nd edition, volume 2.

Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 2nd edition, volume 1.

Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 1st edition, volume 2.

This is a text on games and how to play them intelligently. In this volume, the authors examine games played in clubs, giving case studies for coin and paper-and-pencil games, such as Dots-and-Boxes and Nimstring. Winning Ways for Your Mathematical Plays: First edition divides the content into two volumes. Second edition is comprised of four volumes. This is the 1st edition, volume 1.

"Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, together with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers."--Jacket.