what are the properties of a Napoleon triangle?

Answer 1

" 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."


http://en.wikipedia.org/wiki/Napoleon%27s_theorem

Answer 2

In mathematics, Napoleon's theorem is a theorem that 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.

Although he is traditionally given the credit, there is no specific evidence that Napoleon Bonaparte discovered or proved the theorem.