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 A178816 Decimal expansion of the area of the regular 10-gon (decagon) of edge length 1. 10
 7, 6, 9, 4, 2, 0, 8, 8, 4, 2, 9, 3, 8, 1, 3, 3, 5, 0, 6, 4, 2, 5, 7, 2, 6, 4, 4, 0, 0, 9, 2, 2, 7, 4, 5, 6, 0, 0, 1, 6, 7, 5, 5, 3, 5, 8, 8, 4, 4, 4, 8, 1, 0, 6, 7, 5, 9, 7, 8, 9, 0, 6, 2, 5, 9, 3, 7, 1, 5, 8, 2, 2, 1, 2, 3, 7, 7, 2, 7, 2, 9, 6, 1, 3, 6, 4, 8, 4, 3, 0, 4, 1, 6, 7, 7, 6, 3, 5, 8, 8, 1, 7, 9, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS An algebraic number with degree 4 and denominator 2; minimal polynomial 16x^4 - 1000x^2 + 3125. - Charles R Greathouse IV, Apr 25 2016 This equals in a regular pentagon inscribed in a unit circle with vertices V0 = (x, y) = (1, 0), and V1..V4 in the counterclockwise sense, one tenth of the y-coordinate of the midpoint of side (V1,V2), named M1: M1_y = (2*sqrt(3 - phi) + sqrt(7 - 4*phi))/4 = sqrt(3 + 4*phi)/4. The x-coordinate is M1_x = -1/4. - Wolfdieter Lang, Jan 09 2018 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10001 Wikipedia, Decagon Wikipedia, Regular polygon FORMULA Digits of 5*sqrt(5+2*sqrt(5))/2 = (5/2)*sqrt(3 + 4*phi), with phi from A001622. EXAMPLE 7.69420884293813350642572644009227456001675535884448106759789062593715... sqrt(3 + 4*phi)/4 = 0.769420884293813350642572644009227456001675535884... - Wolfdieter Lang, Jan 09 2018 MAPLE evalf[120](5*sqrt(5+2*sqrt(5))/2); # Muniru A Asiru, Jan 22 2019 MATHEMATICA RealDigits[5*Sqrt[5+2*Sqrt[5]]/2, 10, 100][[1]] PROG (PARI) 5*sqrt(2*sqrt(5)+5)/2 \\ Charles R Greathouse IV, Apr 25 2016 (MAGMA) SetDefaultRealField(RealField(100)); 5*Sqrt(2*Sqrt(5)+5)/2; // G. C. Greubel, Jan 22 2019 (Sage) numerical_approx(5*sqrt(2*sqrt(5)+5)/2, digits=100) # G. C. Greubel, Jan 22 2019 CROSSREFS Cf. Areas of other regular polygons: A120011, A102771, A104956, A178817, A090488, A256853, A256854, A178809. Cf. A001622. Sequence in context: A219705 A273066 A257964 * A200106 A201766 A307951 Adjacent sequences:  A178813 A178814 A178815 * A178817 A178818 A178819 KEYWORD nonn,cons,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Jun 16 2010 STATUS approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)