A273637 -id:A273637 - cp's OEIS frontend

A273633 Decimal expansion of (Pi/(6*sqrt(3)))^(1/3), the sphericity of the tetrahedron.

6, 7, 1, 1, 3, 9, 2, 9, 1, 3, 1, 2, 8, 5, 0, 3, 6, 9, 4, 9, 2, 0, 2, 9, 0, 6, 1, 6, 6, 4, 4, 4, 5, 1, 3, 1, 7, 5, 7, 9, 1, 6, 8, 4, 6, 2, 0, 7, 4, 7, 5, 1, 2, 4, 2, 1, 3, 8, 9, 9, 7, 1, 2, 6, 7, 8, 2, 0, 5, 8, 2, 9, 1, 3, 6, 9, 7, 5, 9, 4, 5, 1, 6, 2, 4, 0

Offset: 0

Felix Fröhlich, May 27 2016

			0.67113929131285036949202906166444513175791684620747512421389971...

Wikipedia, Sphericity.
Index entries for transcendental numbers.

Cf. A093766, A273634, A273635, A273636, A273637.

RealDigits[Surd[Pi/(6*Sqrt[3]), 3], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

default(realprecision, 50080); my(x=(Pi/(6*sqrt(3)))^(1/3)); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; print1(d, ", "))

Equals cube root of A093766. - Michel Marcus, May 27 2016

Definition corrected by Georg Fischer, Jul 12 2021

A273634 Decimal expansion of (Pi/6)^(1/3), the sphericity of the cube.

Original entry on oeis.org

8, 0, 5, 9, 9, 5, 9, 7, 7, 0, 0, 8, 2, 3, 4, 8, 2, 0, 3, 5, 8, 4, 8, 3, 4, 2, 3, 3, 1, 9, 6, 4, 2, 4, 6, 9, 4, 7, 2, 3, 0, 7, 0, 3, 6, 1, 6, 1, 9, 3, 0, 7, 7, 7, 8, 4, 6, 1, 4, 6, 0, 3, 7, 6, 8, 9, 4, 7, 5, 4, 8, 2, 5, 2, 8, 5, 7, 2, 6, 3, 7, 1, 2, 3, 0, 7

Offset: 0

Felix Fröhlich, May 27 2016

			0.80599597700823482035848342331964246947230703616193077784614603...

Wikipedia, Sphericity.
Index entries for transcendental numbers.

Cf. A019673, A273633, A273635, A273636, A273637.

RealDigits[Surd[Pi/6, 3], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

default(realprecision, 50080); my(x=(Pi/6)^(1/3)); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; print1(d, ", "))

Equals cube root of A019673. - Michel Marcus, May 27 2016

A273635 Decimal expansion of (Pi/(3*sqrt(3)))^(1/3), the sphericity of the octahedron.

Original entry on oeis.org

8, 4, 5, 5, 8, 2, 5, 2, 0, 5, 3, 6, 5, 8, 7, 5, 6, 6, 3, 2, 7, 1, 8, 8, 1, 5, 9, 7, 7, 3, 0, 6, 6, 2, 5, 2, 5, 0, 2, 0, 0, 6, 6, 8, 2, 3, 4, 0, 8, 5, 9, 5, 9, 8, 0, 0, 6, 9, 9, 6, 1, 1, 2, 7, 1, 0, 3, 1, 1, 8, 7, 5, 0, 8, 7, 4, 5, 5, 8, 8, 3, 0, 2, 6, 7, 4

Offset: 0

Felix Fröhlich, May 27 2016

			0.84558252053658756632718815977306625250200668234085959800699611...

Wikipedia, Sphericity.
Index entries for transcendental numbers

Cf. A093602, A273633, A273634, A273636, A273637.

RealDigits[Surd[Pi/(3Sqrt[3]),3],10,120][[1]] (* Harvey P. Dale, Jan 07 2023 *)

default(realprecision, 50080); my(x=(Pi/(3*sqrt(3)))^(1/3)); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; print1(d, ", "))

Equals cube root of A093602. - Michel Marcus, May 27 2016

Definition corrected by Georg Fischer, Jul 12 2021

A273636 Decimal expansion of ((Pi(15+7sqrt(5))^2)/(12(25+10sqrt(5))^(3/2)))^(1/3), the sphericity of the dodecahedron.

Original entry on oeis.org

9, 1, 0, 4, 5, 3, 1, 8, 1, 4, 0, 9, 2, 4, 2, 2, 7, 9, 1, 6, 9, 5, 3, 8, 0, 3, 4, 4, 6, 6, 2, 5, 8, 6, 2, 8, 5, 7, 4, 5, 8, 6, 5, 8, 0, 2, 9, 4, 3, 3, 8, 0, 1, 2, 6, 5, 0, 6, 1, 5, 5, 4, 9, 9, 2, 1, 3, 6, 4, 6, 6, 2, 5, 0, 0, 5, 2, 6, 4, 8, 2, 1, 0, 7, 1, 1

Offset: 0

Felix Fröhlich, May 27 2016

			0.91045318140924227916953803446625862857458658029433801265061554...

Wikipedia, Sphericity.
Index entries for transcendental numbers.

Cf. A273633, A273634, A273635, A273637.

RealDigits[((Pi*(15 + 7*Sqrt[5])^2)/(12*(25 + 10*Sqrt[5])^(3/2)))^(1/3), 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

default(realprecision, 50080); my(x=((Pi*(15+7*sqrt(5))^2)/(12*(25+10*sqrt(5))^(3/2)))^(1/3)); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; print1(d, ", "))

A381672 Decimal expansion of the isoperimetric quotient of a regular icosahedron.

Original entry on oeis.org

8, 2, 8, 7, 9, 7, 7, 1, 9, 2, 5, 2, 0, 1, 2, 0, 2, 1, 5, 0, 0, 5, 8, 1, 0, 0, 3, 8, 1, 2, 9, 6, 3, 5, 7, 5, 8, 6, 1, 7, 8, 3, 0, 3, 0, 8, 7, 2, 3, 3, 8, 2, 6, 7, 7, 4, 6, 4, 0, 7, 0, 4, 6, 1, 9, 3, 7, 9, 8, 9, 9, 5, 0, 2, 1, 0, 8, 1, 9, 4, 0, 5, 9, 0, 0, 8, 8, 0, 5, 8

Offset: 0

Paolo Xausa, Mar 03 2025

For the definition of isoperimetric quotient of a solid, see A381671.

			0.8287977192520120215005810038129635758617830308723...

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A273637 (sphericity).
Cf. isoperimetric quotient of other Platonic solids: A019673 (cube), A073010 (octahedron), A374772 (dodecahedron), A381671 (tetrahedron).
Cf. A000796, A002194, A374883.

First[RealDigits[Pi*GoldenRatio^4/(15*Sqrt[3]), 10, 100]]

Equals Pi*phi^4/(15*sqrt(3)) = A000796*A374883/(15*A002194).

cp's OEIS Frontend

A273633 Decimal expansion of (Pi/(6*sqrt(3)))^(1/3), the sphericity of the tetrahedron.

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A273634 Decimal expansion of (Pi/6)^(1/3), the sphericity of the cube.

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A273635 Decimal expansion of (Pi/(3*sqrt(3)))^(1/3), the sphericity of the octahedron.

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A273636 Decimal expansion of ((Pi*(15+7*sqrt(5))^2)/(12*(25+10*sqrt(5))^(3/2)))^(1/3), the sphericity of the dodecahedron.

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A381672 Decimal expansion of the isoperimetric quotient of a regular icosahedron.

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A273636 Decimal expansion of ((Pi(15+7sqrt(5))^2)/(12(25+10sqrt(5))^(3/2)))^(1/3), the sphericity of the dodecahedron.