Hello Alex, A short time ago in Mathworld I came across
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Amazingly, the difference between the areas of the outer and inner Napoleon triangles equals the area of the original triangle (Wells 1991, p. 156).
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As Johnny Carson used to say 'I did not know that.'
But this is not the reason I write this post.
This fact is a fine raw material for P. theorem proof.
Maybe someone will take pains to prove that the sides
of squares equivalent in area to two Napoleons and the
referrence triangle make a right triangle.
Would make a nice addition to the list, would it not?
Salute,
Maj. Pestich