kanner@tymix.UUCP (Herb Kanner) (07/25/84)
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 extraordinally close approximations? I have confirmed it to 14 places. If it is exact, can anyone out there supply a proof?
ljdickey@watmath.UUCP (Lee Dickey) (08/10/84)
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.
ljdickey@watmath.UUCP (Lee Dickey) (08/10/84)
> 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? The relation is exact, and not too dificult to prove. If you want the proof, write to me.