A381152 Decimal expansion of the isoperimetric quotient of a regular pentagon.

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

Offset

0,1

Comments

The isoperimetric quotient of a closed curve is equal to 4*Pi*A/p^2, where A is the area enclosed by the curve and p is its perimeter. For a regular n-gon, this is equivalent to Pi/(n*tan(Pi/n)).

The isoperimetric quotient of a circle is 1.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Isoperimetric Quotient.

Wikipedia, Isoperimetric inequality.

Index entries for transcendental numbers.

Formula

Equals Pi/(5*tan(Pi/5)) = (Pi/5)*A019952.

Equals (4/25)*Pi*A102771.

Example

0.86480626597720996723118206585862333703828555690228...

Mathematica

First[RealDigits[Pi/(5*Tan[Pi/5]), 10, 100]]

Prog

(PARI) Pi/(5*tan(Pi/5)) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A019952, A102771.

Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon), A381157 (12-gon).

Sequence in context: A219863 A340209 A021906 * A154187 A011329 A092033

Adjacent sequences: A381149 A381150 A381151 * A381153 A381154 A381155

Keyword

nonn,cons,easy

Author

Paolo Xausa, Feb 15 2025

Status

approved