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A275967 Decimal expansion of the area cut out by a rotating regular pentagon of width 1 inside a unit square. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,cons
AUTHOR
Jeremy Tan, Aug 14 2016
STATUS
approved

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Last modified June 13 09:43 EDT 2024. Contains 373383 sequences. (Running on oeis4.)