9 Mar
2005
9 Mar
'05
7:13 p.m.
On Thursday 10 March 2005 00:34, Daniel Asimov wrote: [Ed Pegg:]
Richard Sabey's spectacular approximation to e, (1+9-47*6)3285, gets 18457734525360901453873570 decimal digits of accuracy due to high exponents and asymptotic effects.
[Dan:]
Since this is (1 + (very small))^(very large), and since e = lim_(t -> oo) (1 + 1/t)^t, and (1 + 1/t)^t is monotonic increasing for t > 1, this approximation suggests that9^(4^(7*6)) and 3^(2^85) must be fairly good approximations to one another.
Um, yes. *Very* good approximations. In fact ... -- g