English: Geometric demonstration of a rectangle - divided into a square minus a smaller square

The animated sequence shows:

• An initial rectangle (Any dimensions)
• It finds the largest contained square
• It divides the remainder rectangle in half and cuts it there.
• It move the cut rectangle section onto the bottom side.
• The resulting shape is a large square with a small square missing.

Algebraically:

• A rectangle A by B

Is divided into

• A square of length: (A+B)/2
• A missing square of length: abs(A-B)/2

This relation allows any multiplication to be transformed into the difference of two squares.

A x B = [(A+B)/2]^2 - [(A-B)/2]^2