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picture1_Geometry Pdf 166499 | Napoleon Revisited Rigby


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File: Geometry Pdf 166499 | Napoleon Revisited Rigby
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 ...

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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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...Journal of geometry vol c birkh user verlag basel napoleon revisited dedicated to h s m coxeter on the occasion his th birthday j f rigby theorem can be neatly proved using a tessellation plane generalized by three similar triangles instead equilateral erected in different ways sides triangle various interesting special cases occur i there is well known attributed bonaparte although authors doubt possibility knowing enough prove result stated as follows if are externally or internally any their centres form an figure ia...

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