A102525 - OEIS

%I #30 Feb 02 2023 08:34:29

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

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

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

%N Decimal expansion of log(2)/log(3).

%C log_3(2) is the Hausdorff dimension of the Cantor set.

%C Comment from _Stanislav Sykora_, Apr 19 2016: Twice this value is the Hausdorff dimension of the Koch curve, as well as of the 2D Cantor dust. Three times its value is the Hausdorff dimension of the Sierpinski carpet, as well as of the 3D Cantor dust. More in general, N times its value is the Hausdorff dimension of N-dimensional Cantor dust. This number is known to be transcendental.

%D K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985, see p. 14.

%D G. H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 5th Edition, Oxford University Press, ISBN 978-0198531715, 1979, p. 162.

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

%H Turnbull WWW Server, <a href="http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hausdorff.html">Felix Hausdorff</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CantorSet.html">Cantor Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TranscendentalNumber.html">Transcendental Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cantor_set">Cantor set</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hausdorff_dimension">Hausdorff dimension</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension">List of fractals by Hausdorff dimension</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Koch_snowflake">Koch snowflake</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sierpinski_carpet">Sierpinski carpet</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A100831 / 2.

%F Equals 1 / A020857. - _Bernard Schott_, Feb 02 2023

%e log(2)/log(3) = 0.63092975357145743709952711434276085429958564...

%p evalf(log(2)/log(3),100); # _Bernard Schott_, Feb 02 2023

%t RealDigits[Log[3, 2], 10, 111][[1]]

%o (PARI) log(2)/log(3) \\ _Altug Alkan_, Apr 19 2016

%Y Cf. A020857, A100831.

%K cons,nonn

%O 0,1

%A _Robert G. Wilson v_, Jan 13 2005