A179587 Decimal expansion of the volume of square cupola with edge length 1.

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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Keywords

• nonn
• cons
• easy

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

Examples

			1.942809041582063365867792482806465385713114583584632048784453158660...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• 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
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A224268.

Cf. A131594 (decimal expansion of sqrt(2)/3).

Programs

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 *)

PARI

sqrt(8)/3+1 \\ Charles R Greathouse IV, Nov 14 2016

Formula

Equals (3 + 2*sqrt(2))/3.

Equals 1 + 2*A131594. - L. Edson Jeffery, Nov 12 2014