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

1,2

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

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.

Polytope Wiki, Square cupola.

Eric Weisstein's World of Mathematics, Square Cupola.

Wikipedia, Square cupola.

Wolfram Alpha, Johnson solid 4.

Index entries for algebraic numbers, degree 2.

Formula

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

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

Minimal polynomial: 9*x^2 - 18*x + 1. - Amiram Eldar, May 12 2026

Example

1.942809041582063365867792482806465385713114583584632048784453158660...

Mathematica

RealDigits[N[1+(2*Sqrt[2])/3, 200]]
(* Alternative: 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. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A224268.

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

Sequence in context: A099879 A351829 A126774 * A223709 A050016 A377849

Adjacent sequences: A179584 A179585 A179586 * A179588 A179589 A179590

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved