OFFSET
1,1
COMMENTS
Given a circle of area 2n partitioned into n regions by the chords from 1 to each of the n-th roots of unity, 4*cosh^2(Pi/sqrt(12)) gives the product of the area of the parts as the number of parts goes to infinity.
LINKS
Math Stack Exchange user Dan, Product of areas in a circle.
FORMULA
Limit_{n->oo} Product_{k=1..n} (2 - n/Pi*sin(2*k*Pi/n)+n/Pi*sin(2*(k-1)*Pi/n)).
EXAMPLE
8.29674094105780802439644...
MATHEMATICA
RealDigits[4 Cosh[Pi/Sqrt[12]]^2, 10, 100][[1]]
PROG
(PARI) 4*cosh(Pi/sqrt(12))^2 \\ Michel Marcus, Dec 17 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Kagey, Dec 15 2022
STATUS
approved