A178816 - OEIS

A178816

Decimal expansion of the area of the regular 10-gon (decagon) of edge length 1.

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

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OFFSET

1,1

COMMENTS

An algebraic number with degree 4 and denominator 2; minimal polynomial 16x^4 - 1000x^2 + 3125. - Charles R Greathouse IV, Apr 25 2016

This equals in a regular pentagon inscribed in a unit circle with vertices V0 = (x, y) = (1, 0), and V1..V4 in the counterclockwise sense, one tenth of the y-coordinate of the midpoint of side (V1,V2), named M1: M1_y = (2*sqrt(3 - phi) + sqrt(7 - 4*phi))/4 = sqrt(3 + 4*phi)/4. The x-coordinate is M1_x = -1/4. - Wolfdieter Lang, Jan 09 2018

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10001

Wikipedia, Decagon

Wikipedia, Regular polygon

Index entries for algebraic numbers, degree 4

FORMULA

Digits of 5*sqrt(5+2*sqrt(5))/2 = (5/2)*sqrt(3 + 4*phi), with phi from A001622.

EXAMPLE

7.69420884293813350642572644009227456001675535884448106759789062593715...

sqrt(3 + 4*phi)/4 = 0.769420884293813350642572644009227456001675535884... - Wolfdieter Lang, Jan 09 2018

MAPLE

evalf[120](5*sqrt(5+2*sqrt(5))/2); # Muniru A Asiru, Jan 22 2019