Intuitive

The Pythagorean theorem states a relationship between the three sides of a right-angled triangle where $a$ and $b$ represent the sides that form the right angle and $c$ is the longest side.

Concrete

$p^2+q^2=r^2$ if and only if the triangle is a right triangle

Abstract

Why is it interesting?

The Pythagorean theorem enables us to draw accurate maps. This is achieved by covering the area that should be mapped with a virtual network of triangles. These triangles, via the Pythagorean theorem, allow us to measure distances and angles between stretches of land. This method is known as triangulation.