# Trigonometry/Circles and Triangles/Napoleon's theorem

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**Napoleon's theorem** (so called because some people have attributed it to Napoleon Bonaparte) states that if any triangle is taken, and an equilateral triangle constructed on each side, pointing outwards, the centroids of these three triangles are the vertices of an equilateral triangle.

The theorem is easily proved by calculating the separations of the centroids and showing that they are equal.