A104955 Decimal expansion of the area of the regular 5-gon (pentagon) of circumradius = 1.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005

Keywords

• nonn
• cons

Comments

Equivalently, the area in the complex plane of the smallest convex set containing all order-5 roots of unity.

Examples

			2.377641290737883930291098333448455358514246585314375556118264111075382925212...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10001
• Eric Weisstein et al., Root of Unity.
• Eric Weisstein's World of Mathematics, de Moivre Number.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A104954, A104956, A104957.

Programs

Mathematica

Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 5
RealDigits[(5(Sqrt[(5+Sqrt[5])/2]))/4,10,120][[1]] (* Harvey P. Dale, Jul 21 2013 *)

PARI

(5*sqrt((5 + sqrt(5))/2))/4 \\ Michel Marcus, Feb 24 2023

Formula

Equals (5*sqrt((5 + sqrt(5))/2))/4.