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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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