Re: Transcendental Dimensions

gsax wrote: 
Hi

 While playing with fractals, I noticed that I am usually able to
create an equation, such that the dimension of the fractal is a root of
that equation...

 I am therefore skeptical regarding any object having transcendental
dimensions. I mean how would we go about proving that the dimension of
an object is not the root of any integer polynomial...

maybe I am wrong, & if I am I would like to know some examples of
objects with transcendental dimensions.

thanks
Gsax


Try the standard Cantor "middle-thirds" set. Its Hausdorff dimension
is log(2)/log(3), which is transcendental, see this page:

	http://numbers.computation.free.fr/
	    Constants/Miscellaneous/classification.html#Hardy

(the two lines need to be reattached to make a real URL).

The author ascribes the proof that log(3)/log(2) is transcendental
to Hardy and Wright.

Dale.
.

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