The above titled as applicable to self-similar fractals and satisfying real number exponents respectively. This I first noticed in an exploration of rhombic area units and the postulate that for any triangle ABC where c* is the long leg, an exponent ℝ exists that will satisfy a ℝ + b ℝ = c ℝ of non-Diophantine concern (*alternatively, a ℝ + b ℝ = c ℝ can be re-written b ℝ – a ℝ = c ℝ at the isosceles inversion to maintain constancy of convention). The power required in the Pythagorean analogy when happens also to be the fractal dimension of the Koch Curve. The analogous Pythagorean generalization of from: and the fractal dimension from: Since always an isosceles condition or 1:1 ab ratio exists, then from:...
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