A359086 - OEIS

%I #12 Dec 21 2022 20:44:39

%S 8,2,9,6,7,4,0,9,4,1,0,5,7,8,0,8,0,2,4,3,9,6,4,4,0,3,2,0,9,1,2,7,2,6,

%T 0,0,0,3,9,2,3,2,0,5,0,8,1,7,2,9,0,5,2,2,2,0,7,2,2,3,9,8,7,1,3,4,7,2,

%U 9,5,3,2,1,3,6,5,2,5,2,8,6,3,7,7,5,7,0

%N Decimal expansion of 4*cosh^2(Pi/sqrt(12)).

%C 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.

%H Math Stack Exchange user Dan, <a href="https://math.stackexchange.com/questions/4337451/product-of-areas-in-a-circle">Product of areas in a circle</a>.

%F Limit_{n->oo} Product_{k=1..n} (2 - n/Pi*sin(2*k*Pi/n)+n/Pi*sin(2*(k-1)*Pi/n)).

%e 8.29674094105780802439644...

%t RealDigits[4 Cosh[Pi/Sqrt[12]]^2, 10, 100][[1]]

%o (PARI) 4*cosh(Pi/sqrt(12))^2 \\ _Michel Marcus_, Dec 17 2022

%K nonn,cons

%O 1,1

%A _Peter Kagey_, Dec 15 2022