Chapter 10

Hitting the Ends

Folkmar Bornemann


Problem 10


10.1 A First Look: Why Not Monte Carlo? · 10.2 Making It Deterministic · 10.3 Solving It Numerically · 10.4 Solving It Analytically I: Separation of Variables · 10.5 Solving It Analytically II: Conformal Mapping · 10.6 The Joy of Elliptic Functions · 10.7 Finale à la Ramanujan: Singular Moduli · 10.8 Harder Problems

Unexpectedly, there is a closed-form solution:    .
The first 10,002 digits.



A sample path (Figure 10.1 in action)


Historic Sources



This is a web page for the book:

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing. Society of Industrial and Applied Mathematics (SIAM), Philadelphia, 2004.

last modified: 04/23/07 14:41 +0200 (FB)