Napoleon's theorem

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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.

The theorem is often attributed to Napoleon Bonaparte (1769-1821), whence its name, although some sources only trace it back to Dr. W. Rutherford's 1825 publication The Ladies Diary, four years after the French emperor's death.[1]

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

[edit] External links

• Napoleon's Theorem at MathPages
• Napoleon's Theorem and Generalizations
• Napoleon's theorem A proof using the Fermat point without transformations
• To see the construction
• Napoleon's Theorem by Jay Warendorff, The Wolfram Demonstrations Project.
• Eric W. Weisstein, Napoleon's Theorem at MathWorld.