ROSECODE 285
Which one is the best, e or Pi ?
e and Pi are transcendental numbers meaning they cannot be the roots of an algebraic equation with rational coefficients.
So we look for some approximations such that the root of an quadratic equation is as close as possible.
Let the equation be given with the A,B,C triples:
A*x2+B*x+C=0 where A, |B| and |C| are integers <1010 and >0
Find the (Ae,Be,Ce) and (APi,BPi,CPi) triples and corresponding roots (roote and rootPi), and calculate the following ratios:
Re=|e-roote|/e
R? =|Pi-rootPi|/Pi
What are the best triples for e and Pi?
Answer format: Ae,Be,Ce,APi,BPi,CPi (the triples with the smallest ratio)
See also: Transcendental number - Wikipedia, the free encyclopedia
Integer relation algorithm - Wikipedia, the free encyclopedia