Apparently Napoleon Bonaparte came up with this theorem: Return to my Mathematics pages
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© Copyright 2003, Jim Loy
Apparently Napoleon Bonaparte came up with this theorem:
On any triangle, draw equilateral triangles on each side. Then the lines connecting the centers of these equilateral triangles form another equilateral triangle (the one in red here).
This equilateral triangle is called the outer Napoleon triangle.
The theorem also works for the inner
Napoleon triangle (right, in red). Here the equilateral triangles are drawn
toward the inside of the original triangle. And the area of the outer Napoleon
triangle, minus the area of the inner Napoleon triangle, is equal to the area
of the original triangle.
These diagrams were drawn with the program Cinderella.