Napoleon revisited
A classical result (``Napoleon's theorem'') says that if equilateral triangles are erected externally or internally on the side of any triangle in the plane, then their centres form an equilateral triangle. In the present paper, several generalizations of this result are proved; for example, the following is proved: if three similar triangles PCB, CQA, BAR are erected on the sides of any triangle ABC, and if U, V, W are corresponding points of the three triangles, then UVW is similar to the three triangles. By reproducing the triangles we can obtain a tessellation of the plane: properties of these tessellations (and lattice properties of the centres of the triangles) are then considered.
scientific article; zbMATH DE number 4069703