Question

Different methods of proofs on Pythagorean theorem

Answer 1

Professor Edsger W. Dijkstra found an absolutely stunning generalization of the Pythagorean theorem. If, in a triangle, angles a, b, g lie opposite the sides of length a, b, c, then(EWD)sign(a + b - g) = sign(a2 + b2 - c2),where sign(t) is the signum function: sign(t)= -1, for t < 0,sign(0)=  0,sign(t)=  1, for t > 0.The theorem this page is devoted to is treated as "If g = p/2, then a2 + b2 = c2." Dijkstra deservedly finds (EWD) more symmetric and more informative. Absence of transcendental quantities (p) is judged to be an additional advantage.