Dissecting a Square to Four Squares

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This Demonstration shows how to dissect a square into four squares on the basis of the identity .

Contributed by: Izidor Hafner (March 2013)
Open content licensed under CC BY-NC-SA



This Demonstration illustrates examples of Lagrange's four-square theorem, which states that every positive integer can be written as the sum of at most four squares. The first published proof was given by Lagrange (1736–1813) in 1770.


[1] G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 2002 pp. 88 and 282.

[2] Wikipedia. "Lagrance's Four-Square Theorem." (Feb 22, 2013) en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem.

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