Image:Rectangle to square difference2.gif

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Rectangle_to_square_difference2.gif‎ (48KB, 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


Public domain This image has been (or is hereby) released into the public domain by its author, Tomruen at the English Wikipedia project. This applies worldwide.

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Tomruen grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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