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A247554 Decimal expansion of a(F_5), the maximum inradius of all triangles that lie in a regular pentagon of width 1. 0

%I

%S 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,

%T 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,

%U 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

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

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

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

%e 0.2440155280941711153813744336812161242644369887...

%t 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

%o (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

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

%K nonn,cons

%O 0,1

%A _Jean-Fran├žois Alcover_, Sep 19 2014

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)