A100831 Decimal expansion of log(4)/log(3).

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

Offset

1,2

Comments

log_3(4) is the Hausdorff dimension of the Koch snowflake.

A transcendental number. Also the Hausdorff dimension of 2D Cantor dust (for N-dimensional Cantor dust, see A102525). - Stanislav Sykora, Apr 19 2016

References

Martin Gardner, Aha! Gotcha!, "A Pathological Curve", W. H. Freeman, NY, 1982, p. 77.

Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American, University of Chicago Press, IL, 1983, p. 227.

Martin Gardner, The Colossal Book of Mathematics, W. W. Norton, NY, 2001, p. 322.

Nigel Lesmoir-Gordon, Will Rood and Ralph Edney, Introducing Fractal Geometry, Totem Books USA, Lanham, MD, 2001, p. 28.

Manfred Schroeder, Fractals, Chaos, Power Laws, Freeman, 1991, p. 177.

David Wells, The Penguin Dictionary of Curious and Interesting Geometry, Penguin Books, 1991, pp. 135-136.

Links

Table of n, a(n) for n=1..105.

V. L. Almstrum, Visual Koch (Applet).

Robert Ferreol and Jacques Mandonnet, Koch's Curve.

Florida Atlantic University, Koch's Curve Applet.

P. Kernan, Koch Snowflake.

Kris, Koch Fractal,Koch Snowflake.

Aaron Krowne, PlanetMath.org, Koch curve.

M. L. Lapidus & E. P. J. Pearse, A tube formula for the Koch snowflake curve,with applications to complex dimensions, arXiv:math-ph/0412029, 2004-2005.

Simon Plouffe, log4/log3 to 10000 digits.

Larry Riddle, Koch Curve.

Alain Schuler, Chaos and fractal:the Koch's curve.

Gerard Villemin, Almanac of Numbers, Koch's Curve or Snowflake.

Eric Weisstein's World of Mathematics, Koch Snowflake.

Eric Weisstein's World of Mathematics, Cantor Dust.

Wikipedia, Koch curve.

Index entries for transcendental numbers

Formula

Equals 2*A102525. - Stanislav Sykora, Apr 19 2016

Example

log(4)/log(3) = 1.26185950714291487419905422868552170859917128...

Mathematica

RealDigits[Log[3, 4], 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2005 *)

Prog

(PARI) log(4)/log(3) \\ Altug Alkan, Apr 19 2016

Crossrefs

Cf. A094148, A102525.

Sequence in context: A011041 A363996 A291836 * A136763 A109530 A264789

Adjacent sequences: A100828 A100829 A100830 * A100832 A100833 A100834

Keyword

nonn,cons

Author

Lekraj Beedassy, Jan 07 2005

Extensions

More terms from Robert G. Wilson v, Jan 07 2005

Status

approved