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 centres of those equilateral triangles themselves form an equilateral triangle.

The triangle thus formed is called the Napoleon triangle (inner and outer). The difference in area of these two triangles equals the area of the original triangle.

The theorem is often attributed to Napoleon Bonaparte (1769–1821). However, it may just date back to W. Rutherford's 1825 question published in The Ladies' Diary, four years after the French emperor's death.