Pythagoras theorm in spacetime diagrams?

Question

could anyone pls explain to me why the Pythagoras Theorem is not always positive. Why do we need to put in the minus sign?

Answer 1

In purely mathematical terms its because you are dealing with squares of numbers (a squared + b squared = c squared) So when you are solving this to get from a square you need to take the square root of the squared number. when ever you take a square root you get two answers a + and a -, because + times + = a + and a - times a - also = a +. Example: square root of 25 = +5, and -5.

Answer 2

To every triangle there exist a reflection which is imaginary.
To the pythagorean theorem represents a solution to a real figure and an imaginary one(reflected)
So the square root of the hypothenus yield a positive number for the real triangle and a negative one for the reflected triangle .
This kind of result is called geometrical symmetry....