A010502 -id:A010502 - cp's OEIS frontend

A179047 Decimal expansion of 9*sqrt(3)/4, the area of an equilateral triangle of side length 3.

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 26 2010

			3.89711431702997391043675426838821282562131182107335641312556570376684...

Cf. A002194, A010502, A120011.

a=b=c=3;area=Sqrt[(a+b-c)*(a-b+c)*(-a+b+c)*(a+b+c)]/4;RealDigits[N[area,200]]
RealDigits[9 Sqrt[3]/4,10,120][[1]] (* Harvey P. Dale, Apr 27 2025 *)

A179050 Decimal expansion of 5/(2sqrt(5+2sqrt(5))), area of regular pentagram with base edge length 1.

Original entry on oeis.org

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

Offset: 0

Vladimir Joseph Stephan Orlovsky, Jun 26 2010

An algebraic number of degree 4: the smaller positive root of 16x^4 - 200x^2 + 125. - Charles R Greathouse IV, Dec 03 2012

			0.81229924058226581538967853053783616238725867880368775076951179784168...

Thomas M. Green, Area of Pentagram
Index entries for algebraic numbers, degree 4

Cf. A002194, A010502, A102771, A120011, A179047, A179048, A104956.

a=1;area=5/(2*Sqrt[5+2*Sqrt[5]]);RealDigits[N[area,20]]

5/sqrt(20+8*sqrt(5)) \\ Charles R Greathouse IV, Dec 03 2012

Offset corrected, keyword:cons inserted by R. J. Mathar, Jun 28 2010

Name corrected by Charles R Greathouse IV, Dec 03 2012

A384142 Decimal expansion of the volume of a gyroelongated square bipyramid with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, May 22 2025

The gyroelongated square bipyramid is Johnson solid J_17.

			1.428404502627748400527146549078867927980904164...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated square bipyramid.

Cf. A010502 (surface area).

Cf. A002193, A010474, A179638.

First[RealDigits[(Sqrt[2] + Sqrt[4 + Sqrt[18]])/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J17", "Volume"], 10, 100]]

Equals (sqrt(2) + sqrt(4 + 3*sqrt(2)))/3 = (A002193 + sqrt(4 + A010474))/3.

Equals the largest real root of 81*x^4 - 108*x^2 - 72*x-14.

A386461 Decimal expansion of the surface area of a biaugmented truncated cube with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 23 2025

The biaugmented truncated cube is Johnson solid J_67.

			36.241911729260269564523295159701074096328596018257...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Biaugmented truncated cube.

Cf. A010524 (volume - 9).

Cf. A010469, A010487, A010502, A377342, A385535, A386460.

First[RealDigits[18 + 8*Sqrt[2] + Sqrt[48], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J67", "SurfaceArea"], 10, 100]]

Equals 2*(9 + 4*sqrt(2) + 2*sqrt(3)) = 2*(9 + A010487 + A010469) = 18 + A377342 + A010502.

Equals the largest root of x^4 - 72*x^3 + 1592*x^2 - 10656*x - 2672.

A179048 Decimal expansion of 25*sqrt(3)/4, the area of the equilateral triangle of side 5.

Original entry on oeis.org

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

Offset: 2

Vladimir Joseph Stephan Orlovsky, Jun 26 2010

			10.825317547305483084546539634411702293392532836314878925348793621574581355680..

Cf. A002194, A010502, A120011, A179047.

a=b=c=5;area=Sqrt[(a+b-c)*(a-b+c)*(-a+b+c)*(a+b+c)]/4;RealDigits[N[area,200]]
RealDigits[(25*Sqrt[3])/4,10,120][[1]] (* Harvey P. Dale, May 30 2018 *)

25*sqrt(3)/4 \\ Charles R Greathouse IV, Jun 30 2011

Equals 25*A002194/4.

Offset corrected, keyword:cons inserted - R. J. Mathar, Jun 28 2010

A354128 Decimal expansion of 7 - 4*sqrt(3).

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, May 18 2022

The smallest root of x^2 - 14*x + 1 = 0.

			0.07179676972449082589021463397651...

Nicholas Owad and Anastasiia Tsvietkova, Random meander model for links, arXiv:2205.03451 [math.GT], 2022, p. 13.

Cf. A002194, A010502, A019913 (square root), A354129 (multiplicative inverse).

Mathematica
```
First[RealDigits[N[7-4Sqrt[3],92]]]
```

Equals (2 - sqrt(3))^2 = A019913^2. - Jianing Song, May 27 2022

A381690 Decimal expansion of the isoperimetric quotient of a snub cube (snub cuboctahedron).

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 06 2025

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

			0.8991805073406237668693240204602002492109710905019...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A377602 (surface area), A377603 (volume).

Cf. A000796, A010502, A381684.

First[RealDigits[Pi/(3 + Sqrt[48])^3*Root[4*#^3 - 1128*#^2 + 2154*# - 6241 &, 1], 10, 100]]

Equals 36*Pi*A377603^2/(A377602^3).

Equals (Pi/((3 + 4*sqrt(3))^3))*r = (A000796/((3 + A010502)^3))*r, where r is the real root of 4*x^3 - 1128*x^2 + 2154*x - 6241.

cp's OEIS Frontend

A179047 Decimal expansion of 9*sqrt(3)/4, the area of an equilateral triangle of side length 3.

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A179050 Decimal expansion of 5/(2*sqrt(5+2*sqrt(5))), area of regular pentagram with base edge length 1.

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A384142 Decimal expansion of the volume of a gyroelongated square bipyramid with unit edge.

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A386461 Decimal expansion of the surface area of a biaugmented truncated cube with unit edges.

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A179048 Decimal expansion of 25*sqrt(3)/4, the area of the equilateral triangle of side 5.

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A354128 Decimal expansion of 7 - 4*sqrt(3).

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A381690 Decimal expansion of the isoperimetric quotient of a snub cube (snub cuboctahedron).

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A179050 Decimal expansion of 5/(2sqrt(5+2sqrt(5))), area of regular pentagram with base edge length 1.