Later in the session, you will learn more about the High School Students Institut of Mathematics and Informatics established in 2000 by the Union of Bulgarian Mathematicians on the occasion of the World Year of Mathematics.
October 25, 2014 – Oleg Mushkarov – “Napoleon Polygons”
October 22, 2014 by Metroplex Math Circle
In this talk we discuss a new geometric characterization of the so called Napoleon n-gons characterized by the property that the centers of the regular n-gons erected outwardly on its sides are vertices of a regular n-gon. As a consequence, we obtain a new proof of the well-known theorem of Barlotti-Greber that an n-gon is Napoleon if and only if it is affine-regular. Moreover, we generalize this theorem by obtaining an analytic characterization of the n-gons leading to a regular n-gon after iterating the above construction k times.
The talk is based on a joint work with Prof. T. Andreescu, University of Texas at Dallas and
Prof. V. Georgiev, University of Pisa, Italy accepted for publication in American Mathematical Monthly.