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A179587 Decimal expansion of the volume of square cupola with edge length 1. 16
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=1..infinity} (1-1/(4n+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

LINKS

Table of n, a(n) for n=1..105.

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

Digits of 1+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. 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: A155535 A099879 A126774 * A223709 A050016 A033329

Adjacent sequences:  A179584 A179585 A179586 * A179588 A179589 A179590

KEYWORD

nonn,cons,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

STATUS

approved

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Last modified December 6 08:53 EST 2016. Contains 278775 sequences.