fractals

An Intersection of Fractal Dimension and Pythagorean (et al.) Theorem Generalization | Steve Wait – November 23, 2022

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 point (where leg c becomes equal to leg b) to maintain constancy of convention. This is necessitated as ∠C changes between the degenerate triangle limits of zero and π radians, the transition from obtuse scalene to acute scalene. Constrained by this equation, as triangles of a:b < 1 approach isosceles, ℝ becomes extreme....

Continue reading...