OFFSET
1,1
COMMENTS
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.
It is probably transcendental, though that has not been proved.
LINKS
Ondrej Hrdina, First 50000 digits.
Ondrej Hrdina, In-depth description. [Broken link]
FORMULA
Solution of tan(Pi/x) + sin(Pi/x)*cos(Pi/x) = 2*Pi/x. (No closed-form expression for x exists.)
EXAMPLE
x = 3.18176012927017138762046804951303196421721246349351...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Ondrej Hrdina, Dec 30 2016
EXTENSIONS
More digits from Jon E. Schoenfield, Mar 16 2018
STATUS
approved