The Pythagorean Theorem is wonderful and very multicultural, as it is plain that basic knowledge that the theorem applies to real-world measurement problems is

The Pythagorean Theorem is wonderful and very multicultural, as it is plain that basic knowledge that the theorem applies to real-world measurement problems is much earlier in time than the era of Pythagoras, and interesting demonstrations of the theorem have arisen in several different parts of the world. And the Cut the Knot site, from which this link is kindly submitted, is a wonderful site about mathematics in general and should be known by all readers of Hacker News. 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.shtml http://www.cut-the-knot.org/triangle/pythpar/PTimpliesPP.sht... [2] http://www.regentsprep.org/regents/math/geometry/gp13/Pythag.htm http://www.regentsprep.org/regents/math/geometry/gp13/Pythag... https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid... https://www.physicsforums.com/threads/what-happens-to-the-pythagorean-theorem-in-a-non-euclidean-space.226522/ https://www.physicsforums.com/threads/what-happens-to-the-py...