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

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

1,3

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.

References

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

Links

Table of n, a(n) for n=1..105.

Herta T. Freitag, Problem 3855, School Science and Mathematics, Vol. 81, No. 4 (1981), p. 352; Solution to Problem 3855 by David A. Blaeuer, ibid., Vol. 82, No. 3 (1982), pp. 265-266.

Mathematics Stack Exchange, Area of a five pointed star, 2014.

Wikipedia, Pentagram.

Index entries for algebraic numbers, degree 4

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.

Example

1.12256994144896343110486287949381696894803120580270...

Mathematica

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

Crossrefs

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

Sequence in context: A292726 A258621 A258619 * A118807 A240309 A098507

Adjacent sequences: A348754 A348755 A348756 * A348758 A348759 A348760

Keyword

nonn,cons

Author

Amiram Eldar, Nov 12 2021

Status

approved