No. 53: Sep-Oct 1987
Someone has finally complained about an equality sign in SF#37 namely,
D. Thomas has correctly pointed out that we have here only a very good approximation. Of course, one need not do the actual calculation to prove that it is an approximation, because 2143/22 is a rational fraction which can be expressed as a repeating decimal; whereas pi is irrational.
The number (2143/22)¼ is a discovery of Ramanujan, about whom we heard on p. 000. How did he ever stumble upon this extremely accurate approximation of pi -- one that is accurate to 300 parts in a trillion? N.D. Mermin suggests that Ramanujan may have taken it from the expansion:
If 16,539 is replaced by infinity, Ramanujan's result follows.
(Mermin, N. David; "Pi in the Sky," American Journal of Physics, 55:584, 1987.)