Mathematical Constants

by Steven R. Finch

Dedicated to the memory of Philippe Flajolet

My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. *

My book Mathematical Constants is available for online purchase from Cambridge University Press. It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see several very kind reviews. You can also search the book via Amazon and Google by keyword.)

Here are errata and addenda to the book (last updated 1/22/2016), as well sample essays from the book about integer compositions, optimal stopping and Reuleaux triangles. Here also are recent supplementary materials, organized by topic:

Number Theory and Combinatorics

Bipartite, k-colorable and k-colored graphs (6/5/2003)
Transitive relations, topologies and partial orders (6/5/2003)
Series-parallel networks (7/7/2003)
Two asymptotic series (12/10/2003)
Multiples and divisors (1/27/2004)
Discrepancy and uniformity (2/19/2004)
Unitarism and infinitarism (2/25/2004)
Erdös' minimum overlap problem (7/2/2004)
Planar graph growth constants (8/25/2004)
Tauberian constants (8/30/2004)
Integer partitions (9/22/2004)
Class number theory (5/26/2005)
Quadratic Dirichlet L-series (7/15/2005)
Elliptic curves over Q (10/10/2005)
Modular forms on SL₂(Z) (12/28/2005)
Chebyshev's bias (4/26/2006)
Pattern-avoiding permutations (4/27/2006)
Cyclic group orders (4/28/2006)
Dedekind eta products (1/10/2007)
Series involving arithmetic functions (1/24/2007)
Riemann zeta moments (3/22/2007)
Central binomial coefficients (3/28/2007)
Fractional parts of Bernoulli numbers (4/10/2007)
Products of consecutive-integer ratios (4/19/2007)
Prime number theorem (4/27/2007)
Mertens' formula (5/4/2007)
Cyclotomic polynomials (3/31/2008)
Minkowski-Alkauskas constant (5/6/2008)
Two-colorings of positive integers (5/27/2008)
Signum equations and extremal coefficients (2/7/2009)
Monoids of natural numbers (3/17/2009)
Primitive cusp forms (4/27/2009)
Cubic and quartic characters (6/5/2009)
Distribution of error terms (9/9/2009)
Cilleruelo’s LCM constants (10/16/2013)
Amicable pairs and aliquot sequences (10/31/2013)
Fermat numbers and elite primes (11/12/2013)
Average least nonresidues (12/4/2013)
Apollonian circles with integer curvatures (1/3/2014)
Molteni's composition constant (2/5/2014)
Boolean decision functions (4/22/2015)
Map asymptotics constant (4/25/2015)
Injections, surjections and more (5/7/2015)

Inequalities and Approximation

Hardy-Littlewood maximal inequalities (10/12/2003)
Bessel function zeroes (10/23/2003)
Nash's inequality (11/4/2003)
Uncertainty inequalities (11/7/2003)
Airy function zeroes (7/19/2004)
Projections of minimal norm (11/30/2004)
Bohr's inequality (12/5/2004)
Moduli of continuity (12/22/2004)
Quinn-Rand-Strogatz constant (4/27/2008)
Tsirelson's constant (8/19/2008)
Mathieu eigenvalues (10/7/2008)
Thomas-Fermi model (10/15/2008)
Prandtl-Blasius flow (11/12/2008)
Lane-Ritter-Emden constants (11/30/2008)
Radiative transfer equations (12/30/2008)
Carleman’s inequality (12/17/2013)
Golay-Littlewood problem (3/5/2014)
Online matching coins (3/7/2014)
Toothpicks and live cells (7/21/2015)
Virial coefficients (1/29/2016)
Strong triangle inequality (2/8/2016)

Real and Complex Analysis

Radii in geometric function theory (1/5/2004)
Numerical radii of linear operators (4/5/2005)
Coefficient estimates for univalent functions (12/15/2004)
Planar harmonic mappings (3/29/2005)
Constant of interpolation (4/5/2005)
Dirichlet integral (5/15/2008)
Brachistochrone problem (12/17/2008)
Dyadic UMD constants (3/24/2009)
Power series with restricted coefficients (2/19/2014)
Hankel and Toeplitz determinants (3/17/2014)
Gol'dberg's zero-one constants (5/21/2014)
Electrical capacitance (8/25/2014)
Aissen’s convex set function (9/29/2014)
Condition numbers of matrices (1/6/2015)
Goddard’s rocket problem (6/12/2015)
Swing-up control of a pendulum (7/16/2015)
Zermelo’s navigation problem (3/1/2016)

Probability and Stochastic Processes

Hammersley's path process (4/5/2004)
Moments of sums (4/23/2004)
Ornstein-Uhlenbeck process (5/15/2004)
Zero crossings (5/19/2004)
Variants of Brownian motion (6/12/2004)
Shapes of binary trees (6/24/2004)
Expected lifetimes and inradii (2/23/2005)
Subcritical Galton-Watson trees (3/1/2007)
Continued fraction transformation (5/23/2007)
Continued fraction transformation. II (6/15/2007)
Continued fraction transformation. III (7/1/2007)
Continued fraction transformation. IV (7/18/2007)
Lyapunov exponents (11/19/2007)
Lyapunov exponents. II (11/20/2007)
Lyapunov exponents. III (11/21/2007)
Lyapunov exponents. IV (3/18/2008)
Stars and watermelons (4/26/2008)
Prophet inequalities (5/9/2008)
Excursion durations (5/12/2008)
Gambler's ruin (6/19/2008)
Self-convolutions (3/2/2009)
Newcomb-Benford law (8/17/2011)
Electing a leader (12/18/2013)
Substitution dynamics (1/23/2014)
Biham-Middleton-Levine traffic (2/18/2014)
Contact processes (1/23/2015)
Interpolating between max and sum (4/28/2015)
Mixing time of Markov chains (8/4/2015)
Correlated products (1/5/2016)

Geometry and Topology

Knots, links and tangles (8/8/2003)
Convex lattice polygons (12/18/2003)
Volumes of hyperbolic 3-manifolds (9/5/2004)
Poisson-Voronoi tessellations (3/11/2005)
Optimal escape paths (5/30/2005)
Minkowski-Siegel mass constants (1/9/2005)
Slicing problem (4/5/2005)
Constant of Theodorus (4/9/2005)
Nearest-neighbor graphs (4/25/2008)
Random triangles (1/21/2010)
Random triangles. II (2/9/2010)
Random triangles. III (4/30/2010)
Random triangles. IV (5/14/2010)
Random triangles. V (12/22/2010)
Random triangles. VI (1/7/2011)
Colliding dice probabilities (7/29/2011)
Gergonne-Schwarz surface (4/12/2013)
Partitioning problem (5/3/2013)
Soap film experiments (6/5/2013)
Inflating an inelastic membrane (8/15/2013)
Enumerative geometry (2/24/2014)
Distance-avoiding sets in the plane (3/18/2014)
Fraenkel asymmetry (4/1/2014)

Here are several favorite links: Mathematical Constants and Computation (by X. Gourdon & P. Sebah), MathWorld Constants (by E. Weisstein at Wolfram Research), the Inverse Symbolic Calculator (originally by S. Plouffe & the Borwein brothers), and the On-Line Encyclopedia of Integer Sequences (by N. Sloane).

Here finally is contact information for me. I appreciate your interest!

* In October 2002, an ex-employer demanded that this website (formerly at INRIA) be shut down, and I had no choice but to comply (lapsed links here & here). I am grateful to Cambridge University Press for patiently seeing me through a difficult time (up to June 2003).