A258403 Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.

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

Offset: 1

Author

Jean-François Alcover, May 29 2015

Keywords

• nonn
• cons
• easy

Comments

Quartic number of degree 4 and denominator 2; minimal polynomial 16x^4 - 500x^2 + 3125. - Charles R Greathouse IV, Apr 20 2016

Examples

			2.9389262614623656458435297731953638429882621882157299553613624...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10001
• Eric Weisstein's MathWorld, Decagon
• Wikipedia, Decagon

Crossrefs

Cf. A104954 (triangle), A104955 (pentagon), A104956 (hexagon), A104957 (heptagon).

Cf. A178816 (area of decagon with edge length 1). A182007.

Programs

Mathematica

RealDigits[(5/2)*Sqrt[(5 - Sqrt[5])/2], 10, 101] // First

PARI

(5/2)*sqrt((5 - sqrt(5))/2) \\ Michel Marcus, May 29 2015

Formula

Equals (5/2)*sqrt((5-sqrt(5))/2).

Area formulas from triangle to dodecagon, with circumradius 1:

n-gon area(n) = (1/2)*n*sin(2*Pi/n)

3-gon (3*sqrt(3))/4

4-gon 2

5-gon (5/4)*sqrt((5+sqrt(5))/2)

6-gon (3*sqrt(3))/2

7-gon (7/2)*cos((3*Pi)/14)

8-gon 2*sqrt(2)

9-gon (9/2)*sin((2*Pi)/9)

10-gon (5/2)*sqrt((5-sqrt(5))/2)

11-gon (11/2)*sin((2*Pi)/11)

12-gon 3

This constant is (5/2)*A182007. - Wolfdieter Lang, May 08 2018