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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