non-integer exponents

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

This is in reference to the 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=cos⁡C⨯a{B}_{\left(Re\right)x}=\cos{C}⨯a   B(Re)x=cos⁡πn⨯sin⁡C⨯a{B}_{\left(Re\right)x}=\cos{πn}⨯\sin{C⨯a}   B(Im)y=sin⁡πn⨯sin⁡C⨯a{B}_{\left(Im\right)y}=\sin{πn⨯\sin{C⨯a}}   Thus, B rotates about the (Re)x axis tracing a spiraling, discontinuous spherical path. Loss of continuity from exponent extremity...

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