A Curious Integral
It reminds me of those 'surprising' rational approximations of π where xyz/abc≈π with 7 digits precision and abcd/efgh≈π with 9 digits precision. It's not that surprising when you take into account that abcd/efgh does not save you many digits compared to just writing π out.<p>Somewhat similarly the ±23 chars of<p>"∫ 0 ∞ cos(2x)∏ n 1 ∞ cos(xn)dx"<p>giving 43 digits of another number is not _that_ surprising and in the realm of what you can expect with some likelihood.<p>I expect that one could theoretically find some double integral with less then 25 signs which approximates e^π or ANY number to 50 digits.<p>Now if you find some 20 char expression which approximates another 20 char expression up to 100000 digits and THEN suddenly takes a different turn, that would be really curious. Like those properties of natural numbers which are true for some orders of magnitude before someone found a counter example.