For any triangle A1 B1 C1 where c* is the long leg, an exponent n exists that will satisfy a n + b n = c n of non-Diophantine concern. Vertex trisection of A1 B1 C1 through the proportional center yields areas where B1 C1 D + A1 C1 D = A1 B1 D. Subsequent dilation about the proportional center produces dissimilar quadrilaterals. Ad infinitum, these trapezia can exhibit corresponding conservation of the Pythagorean (et al.) Theorem if for a right triangle and the analogous for those absent perpendicularity. *Alternatively, a n + b n = c n can be re-written b n – a n = c n at the isosceles inversion point...
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