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*.

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 @ mweb.co.za