the 1st Napoleon point is constructed as follows:[br][list][*]Construct an equilateral triangle on each of the sides of the given triangle.[/*][*]Draw a line from each vertex of the original triangle to the centroid of the opposite new triangle.[/*][*]The lines intersect at the first Napoleon point.[/*][/list]The barycentric coordinates of this point depend on the lenghts of the sides of the triangle as well as on the angles.