Hosted by The Math Forum

Problem of the Week 809

Find the Pi

This problem is related to the talk today at Macalester by David Bailey, of NASA Ames. Let

x1 = 1.007184476414676228644760147450
x2 = 0.255412811882995341602757048152
x3 = 0.205002557636423533944150336218
x4 = 0.171317070666497458966732774000
Find integers a_i, with -10 <= a_i <= 10, so that, to 30-digit accuracy,
Pi = a1 x1 + a2 x2 + a3 x3 + a4 x4.
To think about: If you solve this problem, try to estimate the total number of floating-point arithmetic operations your method would require to solve similar problems involving n numbers, with a bound b on the size of the integer coefficients.

-- suggested by David Bailey, NASA

Note: Pi = 3.141592653589793238462643383280...

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998