Napoleon's theorem

In mathematics, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centroids of those equilateral triangles themselves form an equilateral triangle.

The absolute difference in area of the inner and outer Napoleon triangles equals the area of the given triangle.

External links

• Napoleon's Theorem at MathPages
• Napoleon's Theorem and Generalizations
• Napoleon's theorem A proof using the Fermat point without transformations

This article incorporates material from Napoleon's theorem on PlanetMath, which is licensed under the GFDL.

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