

A102771


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


12



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
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OFFSET

1,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pentagon


FORMULA

Equals sqrt(25 + 10*sqrt(5)) / 4.
Equals (3*phi+1)*sqrt(3phi) 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 * A232812 A245740 A318922
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



