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This number, the Product[Cos[Pi/n], {n,3,infinity}]
is the limit of an interesting figure in geometry.: If we take a circle, inscribe a triangle, then incribe another circle inside the triangle, then inscribe a square inside the inner circle, then inscribe another circle inside the square, then inscribe a pentagon…
The radius of this figure (the number of sides of the polygon increase with every step:triangle 3, square 4, pentagon 5, …) approaches a limit: Product[Cos[Pi/n], {n,3,infinity}] Is there any way to get an analytic solution to this? Like this would be the square root of Pi or some combination of radicals and irrational numbers? Anyway, Thanks, Mounitra Chatterji mounitra@seas.ucla.edu
mentioned in december 1995. By Mounitra Chatterji
.1149420448532962007010401574695987428307953372008635168440233965;
maple routine —> product(cos(Pi/n),n=3..infinity);evalf(",64);
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The request was sent by achim flammenkamp on Tue Feb 27 09:05:13 PST 1996
The email address is: achim@mathematik.uni-jena.de
The number is 1.60140224354988761393325 (to 24 digits of precision).
-int(sqrt(x)/log(1-x),x=0..1);