A359086 Decimal expansion of 4*cosh^2(Pi/sqrt(12)).

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

Table of n, a(n) for n=1..87.

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

Sequence in context: A155035 A358183 A154189 * A154459 A258164 A031110

Adjacent sequences: A359083 A359084 A359085 * A359087 A359088 A359089

Keyword

nonn,cons

Author

Peter Kagey, Dec 15 2022

Status

approved