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

Author

Jeremy Tan, Aug 14 2016

Keywords

• nonn
• cons

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

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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