A179587 - OEIS

%I #40 Oct 30 2023 02:05:51

%S 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,

%T 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,

%U 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

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

%C Square cupola: 12 vertices, 20 edges, and 10 faces.

%C Also, decimal expansion of 1 + Product_{n>0} (1-1/(4*n+2)^2). - _Bruno Berselli_, Apr 02 2013

%C 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

%C 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

%H G. C. Greubel, <a href="/A179587/b179587.txt">Table of n, a(n) for n = 1..10000</a>

%H Victor Oxman and Moshe Stupel, <a href="http://forumgeom.fau.edu/FG2013volume13/FG201311index.html">Why are the side lengths of the squares inscribed in a triangle so close to each other?</a>, Forum Geometricorum, Vol. 13 (2013), 113-115.

%H Wolfram Alpha, <a href="http://www.wolframalpha.com/input/?i=Johnson+solid+4">Johnson solid 4</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

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

%F Equals 1 + 2*A131594. - _L. Edson Jeffery_, Nov 12 2014

%e 1.942809041582063365867792482806465385713114583584632048784453158660...

%t RealDigits[N[1+(2*Sqrt[2])/3,200]]

%t (* From the second comment: *) RealDigits[N[1 + Product[1 - 1/(4 n + 2)^2, {n, 1, Infinity}], 110]][[1]] (* _Bruno Berselli_, Apr 02 2013 *)

%o (PARI) sqrt(8)/3+1 \\ _Charles R Greathouse IV_, Nov 14 2016

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

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

%K nonn,cons,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Jul 19 2010