Mathematical Constants II

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Steven R. Finch (Author)

9781108470599, Cambridge University Press

Hardback, published 6 December 2018

782 pages, 79 b/w illus. 32 tables
24.1 x 16 x 4.6 cm, 1.27 kg

'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical Gazette

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.

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

Subject Areas: Maths for scientists [PDE], Combinatorics & graph theory [PBV], Number theory [PBH], Mathematical foundations [PBC]