Sum of squares

In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts:

Euclidean geometry and other inner-product spaces

• The Pythagorean theorem says that the square on the hypotenuse of a right triangle is equal in area to the sum of the squares on the legs.
• Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares)
• The British flag theorem for rectangles equates two sums of two squares
• The parallelogram law equates the sum of the squares of the four sides to the sum of the squares of the diagonals