interesting how if you start with 1 you get a line of slope 1. you can also include all integers. π/4 = 1/2 × 2/2 × 3/2 × 4/4 × 5/6 × 6/6 × 7/6 ... if I've got that right. On Sun, Feb 13, 2011 at 9:36 PM, Bill Gosper <billgosper@gmail.com> wrote:
http://math.ucr.edu/home/baez/week127.html finds in Lennart Berggren, Jonathan Borwein and Peter Borwein, π: A Source Book, Springer-Verlag, New York, 1997, "the following weirdly beautiful formula due to Euler, which unfortunately is not explained:" (Then how can they call it a sourcebook?--rwg)
3 5 7 11 13 17 19 π/2 = - × - × - × -- × -- × -- × -- × ... 2 6 6 10 14 18 18
"Here the numerators are the odd primes, and the denominators are the closest numbers of the form 4n+2." E.g., for 10, 100, ..., 10^6 terms, In[209]:=
Table[Block[{p=2},Nest[N[#*(p=NextPrime[p])/(2+4*Round[(p-2)/4]),9]&,2,10^n]],{n,6}]
Out[209]= {3.10152045, 3.13398462, 3.13772561, 3.14073685, 3.14143290, 3.14157195}
Why the heck?? Was Euler a preincarnation of Ramanujan? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun