A247554 Decimal expansion of a(F_5), the maximum inradius of all triangles that lie in a regular pentagon of width 1.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.19 Circumradius-Inradius Constants, p. 535.

Links

Table of n, a(n) for n=0..100.

Formula

Smallest positive root of the polynomial given in the Mathematica code.

Example

0.2440155280941711153813744336812161242644369887...

Mathematica

a[F5] = Root[5*x^8 - 175*x^7 + 611*x^6 - 816*x^5 + 720*x^4 - 280*x^3 + 160*x^2 - 96*x + 16, x, 1]; RealDigits[a[F5], 10, 101] // First

Prog

(PARI) solve(x=0, 1/4, 5*x^8 - 175*x^7 + 611*x^6 - 816*x^5 + 720*x^4 - 280*x^3 + 160*x^2 - 96*x + 16) \\ Michel Marcus, Sep 19 2014

Crossrefs

Cf. A019827 (a(F_4)(unit square)).

Sequence in context: A258371 A111172 A173556 * A198786 A176531 A198362

Adjacent sequences: A247551 A247552 A247553 * A247555 A247556 A247557

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 19 2014

Status

approved