Abstract

A gnomon is a shape which, when added to a figure, yields a figure that is similar to the original one. Gazalé~[4] conjectured that if the gnomon is a regular polygon and the figure to which it is added is a finite polygon then the gnomon is a triangle or a square. We prove this conjecture to be correct.

Keywords: Gnomon, polygon, tesselation, spiral, discontinuous group action.

MSC: 51M99

Pages:  59$-$64     

Volume  55 ,  Issue  3$-$4 ,  2003