Mathematical constants

著者

• Finch, Steven R.

書誌事項

Mathematical constants

Steven R. Finch

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 94, 169）

Cambridge University Press, 2003-

• [1] : hbk
• 2 : hardback

注記

Includes bibliographical references and indexes

内容説明・目次

巻冊次

[1] : hbk ISBN 9780521818056

内容説明

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.

目次

• Preface
• Notation
• 1. Well-known constants
• 2. Constants associated with number theory
• 3. Constants associated with analytic inequalities
• 4. Constants associated with the approximation of functions
• 5. Constants associated with enumerating discrete structures
• 6. Constants associated with functional iteration
• 7. Constants associated with complex analysis
• 8. Constants associated with geometry
• Table
• Index.

巻冊次

2 : hardback ISBN 9781108470599

内容説明

Famous mathematical constants include the ratio of circular circumference to diameter, = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name 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 the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

目次

• 1. Number theory and combinatorics
• 2. Inequalities and approximation
• 3. Real and complex analysis
• 4. Probability and stochastic processes
• 5. Geometry and topology
• Index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA64117147
• ISBN:
  • 0521818052
  • 9781108470599
• LCCN: 2002074058
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: v.
• 大きさ: 25 cm
• 分類:
  • LCC : QA41
  • DC21 : 513
• 件名:
  • LCSH : Mathematical constants
• 親書誌ID:
  • BA00064663