The famous Napoleon Theorem is stated by Coxeter and Greitzer as follows: If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle.
They continue with a historical anecdote:
It is known that Napoleon Bonaparte was a bit of a mathematician with a great interest in geometry. In fact, there is a story that, before he made himself ruler of the French, he engaged in a 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 became his chief military engineer.Coxeter and Greitzer then remark that Napoleon probably did not know enough geometry to discover Napoleon's Theorem, just as he probably did not know enough English to compose the palindrome often attributed to him: Able was I ere I saw Elba.
The portrait is by Anne-Louis Girodet-Trioson (1767-1824).
H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, Mathematical Association of America, 1967.
A study of the attribution of the theorem to Napoleon, as well as another item, called the problem of Mascheroni and Napoleon is
Christoph J. Scriba, "Wie kommt 'Napoleons Satz' zu seinem namen?" Historia Mathematica, 8 (1981) 458-459.
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