non-integer exponents

Visualizing Exponents of Non-integer Pythagorean Generalization | Steve Wait – August 16, 2022

Reference prior post: Less the Answers, a Couple of Related Questions The extent of validity for non-integer generalization of an + bn = cn are represented by point B of triangle ABC. For integer values of exponent n, triangles of conformance are found in the (Re)x, (Re)y plane. Non-integer exponent triangles exist in (Re)x, (Im)y planes where the angle of the (Im)y plane is defined as increment of 1/π. B(Re)x = cosC × a B(Re)y = cosπn × sinC × a B(Im)y = sinπn × sinC × a Thus, B rotates about the (Re)x axis tracing a spiraling, discontinuous spherical...

Continue reading...