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

1,2

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

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

Example

1.720477400588966922759011977...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A258753 A248363 A220674 * A341798 A232812 A245740

Adjacent sequences: A102768 A102769 A102770 * A102772 A102773 A102774

Keyword

nonn,cons

Author

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

Extensions

Corrected the title. - Stanislav Sykora, Apr 12 2015

Status

approved