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?

https://en.wikipedia.org/wiki/Pythagorean_theorem#Consequences_and_uses_of_the_theorem — Andreas, Jun 14 '18 at 11:36
http://righttrianglemath.blogspot.com/p/why-pythagorean-theorem-is-important.html?m=1 — Peter Szilas, Jun 14 '18 at 12:03

score 1 · Accepted Answer · answered Jun 14 '18 at 11:39

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.

How important is Pythagoras's Theorem?

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