76154443343398399851419383

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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);

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.283265121310307732587685540450858868452123075913479495609303244760289207466703551200728343246718266
1721794706326872389237418265273196389116929121819750888062495294277256191719424273967384545908106616
5124702322513598413388920213387535350692362866707758376138858482266928332718882186473891252470626193
1134162075403008037881499615240658150936661712754874529120769279078826146925069339158824377250780006
81691683658433538480533518043146405030754456294577975558177142447872562829157

There is a pattern in the binary expansion of this number.

The request was sent by B.J. Mares on Sun Dec 3 15:20:18 PST 1995
The email address is: bjmares@teleport.com

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The request was sent by Joe Keane on Sun Sep 10 05:02:26 PDT 1995
The email address is: jgk@netcom.com

The number to be tested is:
1.38432969165678691636600070469187275993602894672280031682863878069088210808356345

The number of correct digits in the number:
79

The hints given by the user:

It's log((3+sqrt(7))/sqrt(2)) or 1/2*arccosh(8).

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