# Pythagoras' theorem

Pythagoras' theorem demonstrated in the case of the
3, 5, 5 triangle (one having sides in the ratio 3:4:5). It can be
seen by inspection that in this case *a*^{2} + *b*^{2} = *c*^{2}. Other right-angled triangles, the ratios
of whose sides can be expressed using only small integers are 5, 12,
13 and 8, 15, 17 triangles. *Right:* The ancient method of
laying out a right angle using a knotted rope was known and used long
before the time of Pythagoras.

Pythagoras' theorem states that the square of the length of the hypotenuse (the longest side) of a right triangle is the sum of the squares
of the lengths of the other two sides. This is usually expressed as *a*^{2} + *b*^{2} = *c*^{2}.