A102771 Decimal expansion of area of a regular pentagon with unit edge length.

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

Offset: 1

Author

Bryan Jacobs (bryanjj(AT)gmail.com), Feb 10 2005

Keywords

• nonn
• cons

Examples

			1.720477400588966922759011977...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentagon
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. Areas of other regular polygons: A120011, A104956, A178817, A090488, A256853, A178816, A256854, A178809.

Programs

Mathematica

RealDigits[(5/4)*Sqrt[GoldenRatio^3/Sqrt[5]], 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *)

PARI

5/(4*tan(Pi/5)) \\ Michel Marcus, Mar 25 2015

Formula

Equals sqrt(25 + 10*sqrt(5)) / 4.

Equals (3*phi+1)*sqrt(3-phi) with the golden section phi = (1 + sqrt(5))/2. - Wolfdieter Lang, Jan 25 2013

Equals 5/(4*tan(Pi/5)). - Michel Marcus, Mar 25 2015

Equals (5/4)*sqrt(phi^3/sqrt(5)). - G. C. Greubel, Jul 03 2017

Extensions

Corrected the title. - Stanislav Sykora, Apr 12 2015