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%I #35 Jun 26 2023 02:21:18
%S 3,1,8,1,7,6,0,1,2,9,2,7,0,1,7,1,3,8,7,6,2,0,4,6,8,0,4,9,5,1,3,0,3,1,
%T 9,6,4,2,1,7,2,1,2,4,6,3,4,9,3,5,1,4,2,1,2,4,5,9,9,4,9,2,3,1,4,9,5,7,
%U 6,8,6,6,1,8,4,0,7,0,3,1,6,5,9,8,3,7,6
%N Decimal expansion of x such that tan(Pi/x) + sin(Pi/x)*cos(Pi/x) = 2*Pi/x.
%C This is the hypothetical number of sides an equilateral polygon would have to have in order to create the same area between it and a circle in both its inscribed and circumscribed forms.
%C It is probably transcendental, though that has not been proved.
%H Ondrej Hrdina, <a href="http://pastebin.com/raw/ELZh63gv">First 50000 digits</a>.
%H Ondrej Hrdina, <a href="https://redd.it/5ky9tx">In-depth description</a>. [Broken link]
%F Solution of tan(Pi/x) + sin(Pi/x)*cos(Pi/x) = 2*Pi/x. (No closed-form expression for x exists.)
%e x = 3.18176012927017138762046804951303196421721246349351...
%t RealDigits[x /. FindRoot[Tan[Pi/x] + Sin[Pi/x] * Cos[Pi/x] == 2*Pi/x,{x, 3},WorkingPrecision->120]][[1]] (* _Amiram Eldar_, Jun 26 2023 *)
%K nonn,cons
%O 1,1
%A _Ondrej Hrdina_, Dec 30 2016
%E More digits from _Jon E. Schoenfield_, Mar 16 2018
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