Transcendental Dimensions

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

.

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