''The Book of Numbers'' is a 1996 mathematics book by John H. Conway and Richard K. Guy. It discusses individual numbers, and types of number, that have proved conceptually significant. Topics include the origin of the nursery rhyme " Hickory Dickory Dock",

figurate number The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The ancient Greek mathemat ...

s, the

Fibonacci sequence In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

, transcendental numbers, the

Metonic cycle The Metonic cycle or enneadecaeteris (from , from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise obser ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, the

complex plane In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, call ...

nimber In mathematics, the nimbers, also called Grundy numbers (not to be confused with Grundy chromatic numbers), are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim. The nimbers are the ordin ...

s, and

surreal number In mathematics, the surreal number system is a total order, totally ordered proper class containing not only the real numbers but also Infinity, infinite and infinitesimal, infinitesimal numbers, respectively larger or smaller in absolute value th ...

s. The Basic Library List Committee of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

has recommended that it be included in undergraduate mathematics libraries.

Reception

Andrew Bremner called the book "a delight" and opined that readers of

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

would appreciate it. A. Robert Pargeter found it "fascinating" both for systematic reading and for browsing, and he recommended that school and college libraries carry it. Sarah Gourlie called the book "organized and enlightening", while observing that some topics were considerably more demanding than others. Likewise, reviewing the book for the Mathematical Association of America, Allen Stenger noted that while the book only presumed knowledge of high-school

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

and

trigonometry Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The fiel ...

, it also in places demanded a "high level of mathematical reasoning". Stenger expected that many readers would be unable to follow all of the explanations unaided. A retrospective by Ezra Brown also commented on the "more than a little sophistication" required to follow some of Conway and Guy's discussions, while finding that the authors' joy "comes through on every page". The MacTutor History of Mathematics Archive quotes a review of this book in its biography of Conway, saying that "the publishers should have been required to post a warning label on the front cover indicating that this book contains extremely addictive material."

References

{{DEFAULTSORT:Book Of Numbers 1996 non-fiction books John Horton Conway Mathematics books