Why can't experiment prove the pythagorean theory?

Question

...that is, measuring 3 sides of a triangle in the lab.

Answer 1

The Pythagorean theorem is proved for plane geometry by using geometric ideas.

An experiment can verify that the proof applies in the real world.

There is actually a fancy angle to this question. In Einstein's theory of gravity (called General Relativity) gravity is a distortion of space and time. So in a gravitational field, the Pythagorean theorem doesn't hold exactly. It's really, really close, but not exact.

An incredibly careful measurement could, in theory, measure a difference from what you expect from the Pythagorean theorem, but the difference is so small for the Earth, that I don't know if anyone has actually been able to do this.

Answer 2

Because experiments cannot prove any mathematical concept. Mathematics is based on logic, and only logical proofs work. Suppose that you constructed a right triangle, and measured the sides to a part in a million, and also had the right angle correct to a part in a million. You grind the numbers, and conclude that the hypotenuse should be 1.0000000 feet. You measure 1.0000012 feet. Have you proved the theorem, or not?

Answer 3

First, the accuracy of the measurement is always in question and, more importantly, it would take an infinite amount of time to check it against the infinite mumber of triangles that can be formed.

Besides, there are over 200 different proofs of Pythagorean Theorem known. Why bother 'verifying' it in a lab?

HTH ☺

Doug