Dissecting an Equilateral Triangle into Four Equilateral Triangles
This Demonstration shows Collison's dissection of an equilateral triangle into four equilateral triangles using the identity .
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.
 G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 2002 p. 96.