cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A232810 Decimal expansion of the surface index of a regular dodecahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 01 2013

Keywords

Comments

Equivalently, the surface area of a regular dodecahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), this one, and A232809 (icosahedron).
An algebraic integer with degree 12 and minimal polynomial x^12 - 18954000x^6 + 425152800000. - Charles R Greathouse IV, Apr 25 2016

Examples

			5.311613997069083669796666701461086337809888399341493422663761...

Links

Crossrefs

Cf. A102769, A131595, A232808 (surface index of a sphere), A232809, A232811, A232812.

Programs

  • Mathematica
    RealDigits[3*Sqrt[25 + 10*Sqrt[5]]/((15 + 7*Sqrt[5])/4)^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)
  • PARI
    3*sqrt(25+10*sqrt(5))/((15+7*sqrt(5))/4)^(2/3) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals 3*sqrt(25+10*sqrt(5))/((15+7*sqrt(5))/4)^(2/3).
Equals A131595/A102769^(2/3).

A232812 Decimal expansion of the surface index of a regular tetrahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 01 2013

Keywords

Comments

Equivalently, the surface area of a regular tetrahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: this one, 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and A232809 (icosahedron).

Examples

			7.20562173105601636005279232409725707779044450935589335...

Links

Crossrefs

Cf. A002194, A020829, A232808 (surface index of a sphere), A232809, A232810, A232811.

Programs

Formula

Equals 2*sqrt(3)*3^(2/3).
Equals A002194/A020829^(2/3).

A232809 Decimal expansion of the surface index of a regular icosahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 01 2013

Keywords

Comments

Equivalently, surface area of a regular icosahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and this one.
An algebraic integer of degree 12 with minimal polynomial x^12 - 41115600x^6 + 765275040000. - Charles R Greathouse IV, Apr 25 2016

Examples

			5.14834855619951564633081294611601906410086411638672414845...

Links

Crossrefs

Cf. A010527, A102208 (solid index of a sphere), A232808, A232810, A232811, A232812.

Programs

  • Mathematica
    RealDigits[5*Sqrt[3]/(5*(3+Sqrt[5])/12)^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)
  • PARI
    5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals 5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3).
Equals 10*A010527/A102208^(2/3).

A232811 Decimal expansion of the surface index of a regular octahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 01 2013

Keywords

Comments

Equivalently, the surface area of a regular octahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), this one, A232810 (dodecahedron), and A232809 (icosahedron).
An algebraic integer of degree 6 with minimal polynomial x^6 - 34992. - Charles R Greathouse IV, Apr 25 2016

Examples

			5.7191057579816194425444539723965629466374425679...

Links

Crossrefs

Cf. A010469, A131594, A232808 (surface index for a sphere), A232809, A232810, A232812.

Programs

Formula

sqrt(3)*6^(2/3).
A010469/A131594^(2/3).

A232813 Decimal expansion of the minimum surface index of a closed cylinder.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 03 2013

Keywords

Comments

Equivalently, the minimum surface area among all closed cylinders (cans) enclosing a unit volume. It is attained when the cylinder is right circular and its height matches the diameter of its base. For evident reasons, this value should be called the 'cannery constant'. Its determination is a nice exercise in elementary analysis.
For a general definition of surface index, see A232808.

Examples

			5.53581044593208525729041163876696408034010879864785498817652692...

Links

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232814 (open cylinders), A232815 (closed cones), A232816 (open cones), A232817 (open tubes).

Programs

  • Mathematica
    RealDigits[3 * Surd[2 * Pi, 3], 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

Formula

Equals (54*Pi)^(1/3) = 3*(2*Pi)^(1/3).

A232814 Decimal expansion of the minimum surface index of a half-open cylinder.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 04 2013

Keywords

Comments

Equivalently, the minimum external surface area among all pots or cups (half-open cylinders) delimiting a unit volume. It is attained when the cylinder is right circular and its height matches the radius of its base. We might call it the 'cooking pot constant'. It minimizes the material needed to make the pot (and also its cooling rate). Its determination is a nice exercise in elementary analysis.
For a general definition of surface index, see A232808.

Examples

			4.3937756626845697890604275817913711752157905668838115230717678...

Links

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232815 (closed cones), A232816 (open cones), A232817 (open tubes).
Cf. A092039.

Programs

  • Mathematica
    RealDigits[3 * Surd[Pi, 3], 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

Formula

Equals 3*Pi^(1/3) = 3*A092039.

A232815 Decimal expansion of the minimum surface index of a closed cone.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 04 2013

Keywords

Comments

Equivalently, minimum surface area among all closed cones enclosing a unit volume. It is attained when the cone is right circular and its height equals the diameter of its base multiplied by sqrt(2). Considering one of the ways of marketing ice cream, we might call it the "frozen cone constant".
For a general definition of surface index, see A232808.

Examples

			6.0929477853795556034363160089487569369107615150472...

Links

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232816 (open cones), A232817 (open tubes).

Programs

  • Mathematica
    RealDigits[Surd[72*Pi,3],10,120][[1]] (* Harvey P. Dale, Jul 13 2015 *)

Formula

Equals (72*Pi)^(1/3) = 6*(Pi/3)^(1/3).

A232816 Decimal expansion of the minimum surface index of an open cone.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 05 2013

Keywords

Comments

Equivalently, minimum external surface area among all open cones (not counting the base) enclosing a unit volume. It is attained when the cone is right circular and its height equals the radius of its base multiplied by sqrt(2). We might call it the 'teepee constant', related to the need to minimize the material needed to construct it.
For a general definition of surface index, see A232808.

Examples

			4.18807794862313812872559720593668811944052758870434968621283...

Links

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232815 (closed cones), A232817 (open tubes).

Programs

  • Mathematica
    RealDigits[3 Sqrt[3]Surd[Pi/6,3],10,120][[1]] (* Harvey P. Dale, Nov 23 2022 *)

Formula

3*sqrt(3)*(Pi/6)^(1/3).

A232817 Decimal expansion of the open-tube surface index constant.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Dec 05 2013

Keywords

Comments

The external surface index of an open-ended cylinder (tube) equals this constant, multiplied by (Length/Diameter)^(1/3).
For a general definition of surface index, see A232808.

Links

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232815 (closed cones), A232816 (open cones).

Programs

  • Mathematica
    RealDigits[2 * Surd[2 * Pi, 3], 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

Formula

Equals (16*Pi)^(1/3) = 2*(2*Pi)^(1/3).
Showing 1-9 of 9 results.

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