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A359086
Decimal expansion of 4*cosh^2(Pi/sqrt(12)).
0
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, 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, 9, 5, 3, 2, 1, 3, 6, 5, 2, 5, 2, 8, 6, 3, 7, 7, 5, 7, 0
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
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
Sequence in context: A155035 A358183 A154189 * A154459 A258164 A031110
KEYWORD
nonn,cons
AUTHOR
Peter Kagey, Dec 15 2022
STATUS
approved