Dissecting an Equilateral Triangle into Four Equilateral Triangles

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This Demonstration shows Collison's dissection of an equilateral triangle into four equilateral triangles using the identity .

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



This is an example of applying 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 p. 96.

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