This is a follow up to the prior post: Visualizing Exponents of Non-integer Pythagorean Generalization For any triangle ABC where c is the long leg, an exponent exists that will satisfy an+bn=cn. Thus, via exponentiation, non-right triangles are subjected to generalization of the Pythagorean (et al.) Theorem. Normalizing c and mapping non-integer exponents to the rotating complex plane provides visualization. For n from 1 to ∞ (degenerate and isosceles respectively) of a given ρ (a:b ratio), all triangles can be simulated. Note that the locus of Pythagoras (n=2) lies in the Rex Rey plane and α represents the angle of...
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