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

Author

Lekraj Beedassy, Jan 07 2005

Keywords

• nonn
• cons

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

Examples

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

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

• 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

Crossrefs

Cf. A094148, A102525.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

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