Image:Rectangle to square difference2.gif
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Rectangle_to_square_difference2.gif (600 × 500 pixel, file size: 47 KB, MIME type: image/gif)
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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
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