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A179587 Decimal expansion of the volume of square cupola with edge length 1. 18
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
Victor Oxman and Moshe Stupel, Why are the side lengths of the squares inscribed in a triangle so close to each other?, Forum Geometricorum, Vol. 13 (2013), 113-115.
Wolfram Alpha, Johnson solid 4
FORMULA
Equals (3 + 2*sqrt(2))/3.
Equals 1 + 2*A131594. - L. Edson Jeffery, Nov 12 2014
EXAMPLE
1.942809041582063365867792482806465385713114583584632048784453158660...
MATHEMATICA
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 *)
PROG
(PARI) sqrt(8)/3+1 \\ Charles R Greathouse IV, Nov 14 2016
CROSSREFS
Cf. A131594 (decimal expansion of sqrt(2)/3).
Sequence in context: A099879 A351829 A126774 * A223709 A050016 A033329
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)