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.

Previous Showing 21-22 of 22 results.

A348757 Decimal expansion of the area of a regular pentagram inscribed in a unit-radius circle.

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Nov 12 2021

Keywords

Comments

An algebraic number of degree 4. The smaller of the two positive roots of the equation 16*x^4 - 2500*x^2 + 3125 = 0.

Examples

			1.12256994144896343110486287949381696894803120580270...

References

  • Robert B. Banks, Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics, Princeton University Press, 2012, p. 15.

Links

Crossrefs

Cf. A001622, A019845, A019916, A019952, A019970, A094874, A104955, A134974, A179050, A188593, A344172.

Programs

  • Mathematica
    RealDigits[5*Sin[Pi/5]/GoldenRatio^2, 10, 100][[1]]

Formula

Equals 5*sin(Pi/5)/phi^2, where phi is the golden ratio (A001622).
Equals 5/(cot(Pi/5) + cot(Pi/10)).
Equals 10*tan(Pi/10)/(3 - tan(Pi/10)^2).
Equals (5/2)*sqrt((25 -11*sqrt(5))/2).
Equals 5*(5 - sqrt(5))/(4*sqrt(5 + 2*sqrt(5))) = A094874 * A179050 = 10 * A094874 / A344172.

A373642 Decimal expansion of Sum_{k>=1} (sin(Pi/k))^(2k).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Jun 12 2024

Keywords

Examples

			0^2 + 1^4 + (0.86602...)^6 + (0.70710..)^8 + (0.58778..)^10 + ... = 1.4895502488138264685841...

Links

Crossrefs

Cf. A269611, A010527 (sin Pi/3), A010503 (sin Pi/4), A019845 (sin Pi/5).

Programs

  • PARI
    sumpos(k = 1, sin(Pi/k)^(2*k)) \\ Amiram Eldar, Aug 20 2024
Previous Showing 21-22 of 22 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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