A275967 Decimal expansion of the area cut out by a rotating regular pentagon of width 1 inside a unit square.

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

Offset

0,1

Comments

The part of the square not cut out is made of four congruent regions, one at each corner. Superficially they look like isosceles right triangles, but their "hypotenuses" curve very slightly outward. The region cut out by the pentagon is therefore concave.

Links

Table of n, a(n) for n=0..101.

Jeremy Tan, Regular pentagon in a square (with derivation of constant)

Formula

A = 1-(sqrt(5)-2)*Pi/10 = 0.92583705761388600837689121233541...

Mathematica

First@ RealDigits@ N[1 - (Sqrt@ 5 - 2)/10 Pi, 120] (* Michael De Vlieger, Aug 15 2016 *)

Prog

(PARI) 1-(sqrt(5)-2)*Pi/10

Crossrefs

Cf. A066666 (rotating Reuleaux triangle in a square).

Sequence in context: A328909 A326924 A328908 * A155799 A021112 A353407

Adjacent sequences: A275964 A275965 A275966 * A275968 A275969 A275970

Keyword

nonn,cons

Author

Jeremy Tan, Aug 14 2016

Status

approved