How important is Pythagoras's Theorem?

Question

Everyone in high school learnt about Pythagoras theorem: $a^2+b^2=c^2$

Why It is so important that we have study it in school?

Answer 1

The Pythagorean theorem gives the distance between two points in a Euclidean space (of any dimension; the $2$-dimensional case from school easily generalises by induction). This is the basis for non-Euclidean distance definitions, such as those physicists need in special and general relativity. Also, the implications for norms on complex numbers, quaternions and octonions have a number of important implications, such as Brahmagupta's identity and Lagrange's four-squares theorem.