Napoleon's theorem

Napoleon Triangle, named after the French general and emperor Napoleon Bonaparte, is a term of the triangle geometry.

Definition

About the sides of a given triangle ABC three equilateral triangles are drawn and entered in each of these, the geometric centers of gravity ( centroids ). The Napoleon triangle is formed by connecting these priorities.

If the equilateral triangles applied outwardly, the focus compound gives the appearance of Napoleon triangle with investment of equilateral triangles inward to get the inside Napoleon Triangle.

The Napoleon triangle is - regardless of the shape of the original triangle - always equilateral.

Whether this phrase was actually found by Napoleon, it is not clear safely.

Properties

The focus of the given triangle coincides with the center of gravity of the exterior Napoleon Triangle and the focus of the interior of Napoleon triangle. By forming the difference of the areas of the exterior Napoleon Triangle and the Inner Napoleon Triangle, we obtain the surface area of the given triangle.

Generalization

If we replace in the definition of the three equilateral triangles by similar isosceles triangles, one speaks of a Kiepert Triangle.