Pythagoras was
a Greek mathematician who lived around 500BC and discovered a significant
fact about right-angled triangles known as his theorem. The area
of the square on the side opposite to the right angle is equal to
the sum of the areas of the squares on the sides forming the right
angle.

Area C = area A + area B which is equivalent to
c^{2} = a^{2} + b^{2}

where a, b and c are the lengths of the sides
of the triangle.

For example, the tiling pattern of right-angled
triangles has square R and square Q each made from 4 tiles
while square P is made from 8 tiles.

It is also true that
whenever the lengths a, b, c of the sides of a triangle satisfy
the relation c^{2} = a^{2} + b^{2} then the triangle is right-angled.
This is the converse of pythagoras' theorem.

For example,

when a = 3, b = 4 and c = 5 then a^{2} + b^{2} = 3^{2} + 4^{2} = 25 = 5^{2}
= c^{2} and the triangle is right-angled.