In geometry, Napoleon points are a pair of special points associated with a plane triangle. It is generally believed that the existence of these points was discovered by Napoleon Bonaparte, the Emperor of the French from 1804 to 1815, but many have questioned this belief.[1] The Napoleon points are triangle centers and they are listed as the points X(17) and X(18) in Clark Kimberling’s Encyclopedia of Triangle Centers.
1. Napoleon Point
Three equilateral triangles are drawn outward from the sides of a given triangle. If the centers of gravity of these triangles are connected to the opposite vertices of the original triangle, the connecting lines intersect at a point, which is the first Napoleon point of the given triangle.
2. Napoleon Point
If you draw the equilateral triangles on the opposite side (inward), you obtain the 2nd Napoleon Point.