The Napoleonic Triangle: A Classic Result
Introduction Given any triangle , suppose we take each side and and construct an equilateral triangle on it. You may notice that given a line segment, there are two ways to construct an equilateral triangle on it (one on each side); we will eventually consider both ways, but for now suppose each triangle is constructed on the outside of , i.e. they do not overlap with . We now consider finding the centers of each of these equilateral triangles, as…