A101263 Decimal expansion of sqrt(2 - sqrt(3)), edge length of a regular dodecagon with circumradius 1.

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

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

It is also smaller positive coordinate of (symmetrical) intersection points of x^2 + y^2 = 4 circle and y = 1/x hyperbola. The bigger coordinate is A188887. - Leszek Lezniak, Sep 18 2018

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487.

Links

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

Eric Weisstein's World of Mathematics, Dodecagon.

Index entries for algebraic numbers, degree 4.

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

Equals i^(5/6) + i^(-5/6). - Gary W. Adamson, Jul 07 2022

From Amiram Eldar, Nov 24 2024: (Start)

Equals A120683 / 2 = 2 * A019824 = 1 / A188887 = exp(-A329247).

Equals (sqrt(3)-1)/sqrt(2).

Equals Product_{k>=1} (1 + (-1)^k/A091999(k)). (End)

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*)
RealDigits[Sqrt[2-Sqrt[3]], 10, 120][[1]] (* Harvey P. Dale, Apr 24 2018 *)

Prog

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

Crossrefs

Cf. A003401, A019824, A019913, A091999, A120683, A188739, A188887, A329247.

Sequence in context: A332343 A035109 A301509 * A187561 A088515 A200638

Adjacent sequences: A101260 A101261 A101262 * A101264 A101265 A101266

Keyword

cons,nonn,changed

Author

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

Status

approved