A381157 Decimal expansion of the isoperimetric quotient of a regular 12-gon.

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

Offset: 0

Author

Paolo Xausa, Feb 15 2025

Keywords

• nonn
• cons
• easy

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.97704861665685333572562679495712274710387812858570...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Isoperimetric Quotient.
• Wikipedia, Isoperimetric inequality.

Crossrefs

Cf. A019913, A178809.

Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon).

Programs

Mathematica

First[RealDigits[Pi/(12*Tan[Pi/12]), 10, 100]]

Formula

Equals Pi/(12*tan(Pi/12)) = Pi/(12*A019913).

Equals (1/36)*Pi*A178809.