A221185 Decimal expansion of sqrt(120-18*sqrt(3))/3.

3, 1, 4, 1, 5, 3, 3, 3, 3, 8, 7, 0, 5, 0, 9, 4, 6, 1, 8, 6, 3, 6, 3, 9, 8, 2, 2, 1, 9, 6, 4, 6, 2, 4, 0, 7, 1, 1, 9, 9, 1, 2, 4, 1, 7, 9, 2, 1, 3, 3, 6, 3, 2, 6, 4, 2, 4, 2, 9, 4, 0, 2, 1, 3, 5, 9, 2, 0, 5, 0, 8, 9, 0, 0, 7, 4, 0, 5, 8, 4, 0, 4, 5, 1, 5, 1, 0, 1, 0, 0, 8, 9, 6, 3, 0, 5, 8, 4, 7, 5, 8, 4, 0, 7, 2, 1, 6, 7, 9, 5, 7, 0, 9, 7, 8, 9, 3, 1, 9, 7, 7

Offset

1,1

Comments

An approximation for Pi, obtained by a geometrical construction by Kochański (1685). - Amiram Eldar, Sep 12 2022

References

Benjamin Bold, Famous Problems of Geometry and How to Solve Them, New York: Dover, 1982, p. 44.

J. L. Heilbron, Geometry Civilized: History, Culture, and Technique, Oxford University Press, 2000, pp. 250-252.

Hugo Steinhaus, Mathematical Snapshots, 3rd ed., New York: Dover, 1999, p. 143.

Links

Table of n, a(n) for n=1..121.

Mordechai Ben-Ari, Mathematical Surprises, Springer, 2022, p. 30.

Henryk Fukś, Adam Adamandy Kochanski's approximations of Pi: reconstruction of the algorithm, Math. Intelligencer, Vol. 34, No. 4 (2012), pp. 40-45; arXiv preprint, arXiv:1111.1739 [math.HO], 2011-2014.

Adam Adamandy Kochański, Observationes Cyclometricae ad facilitandam Praxin accomodatae, Acta Eruditorum, Vol. 4 (1685), pp. 394-398.

Eric Weisstein's World of Mathematics, Kochanski's Approximation.

Example

3.1415333387050946186363982219646240711991241792133632642429...

Mathematica

RealDigits[Sqrt[120 - 18*Sqrt[3]]/3, 10, 100][[1]] (* Amiram Eldar, Sep 12 2022 *)

Prog

(PARI) sqrt(40/3-2*sqrt(3)) \\ Charles R Greathouse IV, Mar 25 2014

Crossrefs

Cf. A199657, A199658, A199671, A199672.

Sequence in context: A363521 A166050 A259655 * A378533 A242746 A363258

Adjacent sequences: A221182 A221183 A221184 * A221186 A221187 A221188

Keyword

nonn,cons

Author

N. J. A. Sloane, Jan 23 2013

Status

approved