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 1-2 of 2 results.

A341332 Decimal expansion of Pi/(2*phi).

Original entry on oeis.org

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

Views

Author

Bernard Schott, Feb 09 2021

Keywords

Comments

This is the middle angle (in radians) of the unique right triangle whose angles are in geometric progression; common ratio is phi and the angles are (Pi/(2*phi^2), Pi/(2*phi), Pi/2) in radians, corresponding to approximately (34.377, 55.623, 90) in degrees.

Examples

			0.970805519362733288673432814981347978817334946923024149753694108...

Links

Crossrefs

Cf. A000796 (Pi), A001622 (phi), A019669 (Pi/2), A180014 (Pi/(2*phi^2)).

Programs

  • Maple
    evalf(Pi/(1+sqrt(5)),150);
  • Mathematica
    RealDigits[Pi/(2*GoldenRatio), 10, 100][[1]] (* Amiram Eldar, Feb 09 2021 *)
  • PARI
    Pi/(1+sqrt(5)) \\ Michel Marcus, Feb 09 2021

Formula

Equals A019669/A001622 = A094881/2 = Pi/(1+sqrt(5)) = (Pi/4) * (sqrt(5)-1).

A193537 Decimal expansion of cos(Pi/(1+phi)), where phi is the golden ratio.

Original entry on oeis.org

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

Views

Author

Frank M Jackson, Jul 29 2011

Keywords

Comments

cos(Pi/(1+phi)) is the first term in the identity:
cos(Pi/(1+phi))+cos(Pi/phi)=0 which when converted to the exponential form gives: e^(i*Pi/(1+phi))+e^(-i*Pi/(1+phi))+e^(i*Pi/phi)+e^(-i*Pi/phi)=0. In this form it is known as the phi identity because it combines the golden ratio phi with the five fundamental mathematical constants Pi, e, i, 1, 0 that are found in Euler's identity e^(i*Pi) + 1 = 0.

Examples

			0.3623748900804801199586466374749868993608655440055985464501567887401235062...

Links

Programs

Formula

c = cos(Pi/(1+phi)) = cos(2*A180014).
Showing 1-2 of 2 results.

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