The sum of squared dimensions of a finite group's pairwise nonequivalent complex representations is equal to cardinality of that group.
Euclidean geometry and other inner-product spacesedit
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. The sum of squares is not factorable.
The squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates
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)