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A101263 Decimal expansion of sqrt(2-sqrt(3)), edge length of a regular dodecagon with circumradius 1. 7
5, 1, 7, 6, 3, 8, 0, 9, 0, 2, 0, 5, 0, 4, 1, 5, 2, 4, 6, 9, 7, 7, 9, 7, 6, 7, 5, 2, 4, 8, 0, 9, 6, 6, 5, 6, 6, 9, 8, 1, 3, 7, 8, 0, 2, 6, 3, 9, 8, 6, 1, 0, 2, 7, 6, 2, 8, 0, 0, 6, 4, 1, 4, 6, 3, 0, 1, 1, 3, 9, 4, 9, 4, 9, 7, 6, 0, 3, 9, 9, 3, 8, 4, 4, 7, 3, 5, 9, 4, 9, 3, 8, 8, 4, 9, 9, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

sqrt(2-sqrt(3)) is the shape of the lesser sqrt(6)-contraction rectangle, as defined at A188739. [Clark Kimberling, Apr 16 2011]

This is a constructible number, since 12-gon is a constructible polygon. See A003401 for more details. - Stanislav Sykora, May 02 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Dodecagon.

FORMULA

Equals sqrt(A019913). - R. J. Mathar, Apr 20 2009

Equals 2*sin(Pi/12) = 2*cos(Pi*5/12). - Stanislav Sykora, May 02 2016

EXAMPLE

0.517638090205041524697797675248096656698137802639861027628006414630113....

MATHEMATICA

r = 6^(1/2); t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]]  (*A101263*)

PROG

(PARI) 2*sin(Pi/12) \\ Stanislav Sykora, May 02 2016

CROSSREFS

Cf. A003401, A188887.

Sequence in context: A198129 A244425 A035109 * A187561 A088515 A200638

Adjacent sequences:  A101260 A101261 A101262 * A101264 A101265 A101266

KEYWORD

cons,nonn

AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 25 2005

STATUS

approved

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Last modified October 19 22:53 EDT 2017. Contains 293600 sequences.