Napoleon's Theorem


Though it's not clear historically whether Napoleon actually discovered and proved the theorem named after him, he was a keen geometer nonetheless. He was once engaged in mathematical discussion with the great mathematicians Lagrange and Laplace until the latter told him, severely: "The last thing we want from you, general, is a lesson in geometry." Laplace later became his chief military engineer. - Coxeter & Greitzer (1967, p. 63), Geometry Revisited.

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Napoleon's Theorem

First try and explain why (prove) it is true yourself. But if you get stuck, have a look at my book, Rethinking Proof with Sketchpad, which contains a discovery of the result and a guided proof (as well as in the Teacher Notes, proofs of the generalizations below). Or alternatively, consult my book available in printed form or PDF download at Some Adventures in Euclidean Geometry.

Then explore the generalizations and variations below, and also try to explain (prove) why they are true.

Generalizations of Napoleon's Theorem

Related Variations of Napoleon's Theorem

Converses of Napoleon's Theorem

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Modified by Michael de Villiers, 7 June 2013 at profmd @