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Journal of Geometry 0047-2468/88/020129-1851.50+0.20/0
Vol. 33 (1988) (c) 1988 Birkh~user Verlag, Basel
NAPOLEON REVISITED
Dedicated to H. S, M. Coxeter on the occasion of his 80th birthday.
J, F. Rigby
Napoleon's Theorem can be neatly proved using a tessellation of the plane, The
theorem can be generalized by using three similar triangles (instead of the three
equilateral triangles) erected in different ways on the three sides of the
triangle. Various interesting special cases occur.
i.
There is a well-known theorem attributed to Napoleon Bonaparte, although the
authors of [4] doubt the possibility of his knowing enough geometry to prove the
result [4, p,63], The theorem can be stated as follows.
THEOREM i.i, If equilateral triangles are erected externally or internally on the
sides of" any triangle, their centres form an equilateral triangle. (Figure IA),
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