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.

The square of the length of the hypotenuse
of a right triangle is the sum of the squares
of the lengths of the two sides. This is usually expressed as a^{2}
+ b^{2} = c^{2}.