Mathematical Constants
Publisher: Cambridge University Press
Published: August 18, 2003
Language: eng
Format: Hardcover
Number of pages: 622
ISBN-13: 9780521818056
Subjects: Combinatorics & graph theory; Mathematical foundations; Mathematics (Specific Aspects); Mathematics; Science/Mathematics; Arithmetic; General; Mathematics / General; Mathematical constants
First sentence: The diagonal of a unit square has length 2 = 1.4142135623....A theory, proposed by the Pythagorean school of philosophy, maintained that all geometric magnitudes could be expressed by rational numbers.
Description: Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14 ..., and the natural logarithmic base, e=2.178 ... Students and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. Topics covered include the statistics of continued fractions, chaos in nonlinear systems, prime numbers, sum-free sets, isoperimetric problems, approximation theory, self-avoiding walks and the Ising model (from statistical physics), binary and digital search trees (from theoretical computer science), the Prouhet-Thue-Morse sequence, complex analysis, geometric probability and the traveling salesman problem. This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Notes: Encyclopedia of Mathematics and its Applications