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 1-6 of 6 results.

A381152 Decimal expansion of the isoperimetric quotient of a regular pentagon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

The isoperimetric quotient of a closed curve is equal to 4*Pi*A/p^2, where A is the area enclosed by the curve and p is its perimeter. For a regular n-gon, this is equivalent to Pi/(n*tan(Pi/n)).
The isoperimetric quotient of a circle is 1.

Examples

			0.86480626597720996723118206585862333703828555690228...

Links

Crossrefs

Cf. A019952, A102771.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon), A381157 (12-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(5*Tan[Pi/5]), 10, 100]]

Formula

Equals Pi/(5*tan(Pi/5)) = (Pi/5)*A019952.
Equals (4/25)*Pi*A102771.

A381153 Decimal expansion of the isoperimetric quotient of a regular heptagon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.93194062349909574595222630089422754574528525154715...

Links

Crossrefs

Cf. A178817, A343058.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon), A381157 (12-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(7*Tan[Pi/7]), 10, 100]]

Formula

Equals Pi/(7*tan(Pi/7)) = Pi/(7*A343058).
Equals (4/49)*Pi*A178817.

A381154 Decimal expansion of the isoperimetric quotient of a regular 9-gon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.959050541873609358074543306708643413020181580975...

Links

Crossrefs

Cf. A019918, A256853.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381155 (10-gon), A381156 (11-gon), A381157 (12-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(9*Tan[Pi/9]), 10, 100]]

Formula

Equals Pi/(9*tan(Pi/9)) = Pi/(9*A019918).
Equals (4/81)*Pi*A256853.

A381155 Decimal expansion of the isoperimetric quotient of a regular 10-gon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.96688279904640254032818321918275298846986824108440...

Links

Crossrefs

Cf. A019916, A178816.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381156 (11-gon), A381157 (12-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(10*Tan[Pi/10]), 10, 100]]

Formula

Equals Pi/(10*tan(Pi/10)) = Pi/(10*A019916).
Equals (1/25)*Pi*A178816.

A381156 Decimal expansion of the isoperimetric quotient of a regular 11-gon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.97266200091990681953828897938526763171296541114234...

Links

Crossrefs

Cf. A256854.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381157 (12-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(11*Tan[Pi/11]), 10, 100]]

Formula

Equals Pi/(11*tan(Pi/11)).
Equals (4/121)*Pi*A256854.

A381157 Decimal expansion of the isoperimetric quotient of a regular 12-gon.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 15 2025

Keywords

Comments

For the definition of isoperimetric quotient, see A381152.

Examples

			0.97704861665685333572562679495712274710387812858570...

Links

Crossrefs

Cf. A019913, A178809.
Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A381152 (pentagon), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon).

Programs

  • Mathematica
    First[RealDigits[Pi/(12*Tan[Pi/12]), 10, 100]]

Formula

Equals Pi/(12*tan(Pi/12)) = Pi/(12*A019913).
Equals (1/36)*Pi*A178809.
Showing 1-6 of 6 results.

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