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From: ljdickey@watmath.UUCP (Lee Dickey)
Newsgroups: net.math
Subject: Re: math identity
Message-ID: <8601@watmath.UUCP>
Date: Fri, 10-Aug-84 09:30:31 EDT
Article-I.D.: watmath.8601
Posted: Fri Aug 10 09:30:31 1984
Date-Received: Sat, 11-Aug-84 00:14:36 EDT
References: <261@tymix.UUCP> <266@tymix.UUCP>
Organization: U of Waterloo, Ontario
Lines: 21

H Kanner (kanner@tymix.uucp) writes:
> The following assertion was found in the curiosity column of a magazine
> addressed to mathematics instructors:
> 
> 	tan(3*pi/11) + 4*sin(2*pi/11) = sqrt(11) exactly, but who cares?
> 
> Is the relation exact, or is it one of those extraordinary coincidences?
> I have confirmed it to 14 places.  If it is a true relation, can anyone
> out there supply a proof?

Here are the first 250 or so places, of the left side, as given by Maple:

lv := 3.316624790355399849114932736670686683927088545589353597058682146116484
64260904384670884339912829065090701255784952745659227543978485754747977932493
30447288473028739748286556825773944446120980444771931123571441329715210988326
60495710037248520738106821

The value of the right hand side, again as given by Maple, differs only
in the last digit; but that difference seems to be a quirk, because changing
the precision only moves the difference to a new, last digit.