Pythagorean Theorem and its many proofs
cut-the-knot.org
cut-the-knot.org
Cut the Knot has another good page, "The Pythagorean Theorem is Equivalent to the Parallel Postulate," pointing out that the conventional form of the Pythagorean Theorem is a theorem only of Euclidean geometry, and the theorem's statement has to be modified in non-Euclidean geometry. I make sure to tell all my students that, even though my students are studying mathematics at the "prealgebra" level and are of middle-elementary-school age (taking supplementary classes for advanced learners). Learning non-Euclidean geometry is harder if early math teachers don't mention that our usual school lessons in geometry assume Euclidean geometry with the parallel postulate is the only possible true description of the world. I like pointing my students to other resources about non-Euclidean geometry and the parallel postulate for possible optional further reading for them or for their parents.[2]
[1] http://www.cut-the-knot.org/triangle/pythpar/PTimpliesPP.sht...
[2] http://www.regentsprep.org/regents/math/geometry/gp13/Pythag...
https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid...
https://www.physicsforums.com/threads/what-happens-to-the-py...
if it is not too inconvenient, may you please link to it ? it would be instructive to see a novel proof of something which has been around for approx. 2500 years. thank you !