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A275967
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Decimal expansion of the area cut out by a rotating regular pentagon of width 1 inside a unit square.
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0
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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A = 1-(sqrt(5)-2)*Pi/10 = 0.92583705761388600837689121233541...
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MATHEMATICA
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PROG
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(PARI) 1-(sqrt(5)-2)*Pi/10
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CROSSREFS
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Cf. A066666 (rotating Reuleaux triangle in a square).
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KEYWORD
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AUTHOR
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STATUS
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approved
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