# Pythagorean theorem

The *Pythagorean theorem* is one of the fundamental theorems of two-dimensional geometry. It states that for all right-angled triangles (cf. Figure 1) the side lengths are in a certain ratio to each other: If one forms a square over each of the three sides, the sum of the areas of the two smaller squares (over the *Cathetes* and ) is exactly as large as the area of the large square (above the *hypotenuse* ). Expressed as an equation, the Pythagorean theorem is therefore simply .