Dissecting an Equilateral Triangle into Four Equilateral Triangles
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 +++=.
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Details
Details
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.
References
References
[1] G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 2002 p. 96.
External Links
External Links
Permanent Citation
Permanent Citation
Izidor Hafner
"Dissecting an Equilateral Triangle into Four Equilateral Triangles"
http://demonstrations.wolfram.com/DissectingAnEquilateralTriangleIntoFourEquilateralTriangles/
Wolfram Demonstrations Project
Published: April 18, 2013