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A179587
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Decimal expansion of the volume of square cupola with edge length 1.
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18
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1, 9, 4, 2, 8, 0, 9, 0, 4, 1, 5, 8, 2, 0, 6, 3, 3, 6, 5, 8, 6, 7, 7, 9, 2, 4, 8, 2, 8, 0, 6, 4, 6, 5, 3, 8, 5, 7, 1, 3, 1, 1, 4, 5, 8, 3, 5, 8, 4, 6, 3, 2, 0, 4, 8, 7, 8, 4, 4, 5, 3, 1, 5, 8, 6, 6, 0, 4, 8, 8, 3, 1, 8, 9, 7, 4, 7, 3, 8, 0, 2, 5, 9, 0, 0, 2, 5, 8, 3, 5, 6, 2, 1, 8, 4, 2, 7, 7, 1, 5, 1, 5, 6, 6, 7
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OFFSET
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1,2
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COMMENTS
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Square cupola: 12 vertices, 20 edges, and 10 faces.
Also, decimal expansion of 1 + Product_{n>0} (1-1/(4*n+2)^2). - Bruno Berselli, Apr 02 2013
Decimal expansion of 1 + (least possible ratio of the side length of one inscribed square to the side length of another inscribed square in the same non-obtuse triangle). - L. Edson Jeffery, Nov 12 2014
2*sqrt(2)/3 is the radius of the base of the maximum-volume right cone inscribed in a unit-radius sphere. - Amiram Eldar, Sep 25 2022
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LINKS
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FORMULA
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Equals (3 + 2*sqrt(2))/3.
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EXAMPLE
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1.942809041582063365867792482806465385713114583584632048784453158660...
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MATHEMATICA
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RealDigits[N[1+(2*Sqrt[2])/3, 200]]
(* From the second comment: *) RealDigits[N[1 + Product[1 - 1/(4 n + 2)^2, {n, 1, Infinity}], 110]][[1]] (* Bruno Berselli, Apr 02 2013 *)
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PROG
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CROSSREFS
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Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A224268.
Cf. A131594 (decimal expansion of sqrt(2)/3).
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KEYWORD
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AUTHOR
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STATUS
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approved
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