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A179290 Decimal expansion of length of edge of a regular icosahedron with radius of circumscribed sphere = 1. 26
1, 0, 5, 1, 4, 6, 2, 2, 2, 4, 2, 3, 8, 2, 6, 7, 2, 1, 2, 0, 5, 1, 3, 3, 8, 1, 6, 9, 6, 9, 5, 7, 5, 3, 2, 1, 4, 5, 7, 0, 9, 9, 5, 8, 6, 4, 4, 8, 6, 6, 8, 3, 5, 6, 3, 0, 5, 7, 8, 7, 1, 0, 4, 6, 4, 8, 2, 4, 2, 2, 2, 9, 2, 8, 0, 6, 4, 2, 8, 0, 3, 6, 7, 4, 3, 2, 6, 5, 2, 5, 7, 6, 6, 3, 1, 0, 5, 1, 4, 1, 9, 1, 3, 3, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Regular icosahedron: A three dimensional figure with 20 congruence equilateral triangle faces, 12 vertices, and 30 edges.

Shorter diagonal of golden rhombus with unit edge length. - Eric W. Weisstein, Dec 11 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..1000

J. Brandts, S. Korotov, M. Krizek, J. Solc, On nonobtuse simplicial partitions, Siam Rev. 51 (2) (2009) 317-335.

Dr. Math, Regular Polyhedra: Formulas

Eric Weisstein's World of Mathematics, Golden Rhombus

Eric Weisstein's World of Mathematics, Icosahedron

Wikipedia, Icosahedron

FORMULA

Equals sqrt(50-10*sqrt(5))/5.

Equals csc(2*Pi/5). - Eric W. Weisstein, Dec 11 2018

Equals 1/Im(e^(3*i*Pi/5)) = 1/Im(e^(3*i*Pi/5) - 1) = sqrt(2 - 2/sqrt(5)). - Karl V. Keller, Jr., Jun 11 2020

EXAMPLE

1.051462224238267212051338169695753214570995864486683563057871046482422...

MAPLE

evalf[120](csc(2*Pi/5)); # Muniru A Asiru, Dec 11 2018

MATHEMATICA

RealDigits[Csc[2 Pi/5], 10, 110][[1]] (* Eric W. Weisstein, Dec 11 2018 *)

PROG

(Python)

from decimal import *

getcontext().prec = 110

c = Decimal.sqrt(2 - 2 / Decimal.sqrt(Decimal(5)))

print([int(i) for i in str(c) if i != '.'])

# Karl V. Keller, Jr., Jul 10 2020

CROSSREFS

Cf. A010527, A102208.

Cf. A179290 (longer golden rhombus diagonal).

Sequence in context: A200022 A216157 A216851 * A167864 A232809 A011301

Adjacent sequences:  A179287 A179288 A179289 * A179291 A179292 A179293

KEYWORD

nonn,cons,easy,changed

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

EXTENSIONS

Partially rewritten by Charles R Greathouse IV, Feb 02 2011

STATUS

approved

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Last modified July 16 12:40 EDT 2020. Contains 335788 sequences. (Running on oeis4.)