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A392340

Decimal expansion of the area of a 15-gon with unit side lengths.

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

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OFFSET

2,2

COMMENTS

The largest positive solution to 65536*x^8 - 25804800*x^6 + 1736640000*x^4 - 16767000000*x^2 + 2562890625 = 0.

This constant multiplied by the square of the side length of a regular 15-gon equals the area of that 15-gon.

15^2 divided by this constant equals 60 * tan(Pi/15) = 12.75339370... which is the perimeter and the area of an equable 15-gon with its side length 4 * tan(Pi/15) = 0.85022624... .

LINKS

Table of n, a(n) for n=2..106.

Eric Weisstein's World of Mathematics, Pentadecagon.

Wikipedia, Pentadecagon.

FORMULA

Equals 15 / (4 * tan(Pi/15)).

Equals 15/4 * sqrt(7 + sqrt(20) + sqrt(60 + sqrt(2880))).

Equals 15/8 * (sqrt(3) + sqrt(15) + sqrt(10 + sqrt(20))).

EXAMPLE

17.6423629105442033...

MAPLE

evalf(15 / (4 * tan(Pi/15)), 105);