WHEN: 18.06.15 at 14:15
WHERE: Seminar Room, Arnimallee 2, FU Berlin

Speaker: Emmanuel Tsukerman (Berkeley)

Circumcenter of mass

I shall define and study a variant of the center of mass of a polygon, called the circumcenter of mass. The circumcenter of mass is an affine combination of the circumcenters of the triangles in a non-degenerate triangulation of a polygon, weighted by their areas, and is independent of the triangulation. It satisfies an analog of the Archimedes Lemma, similarly to the center of mass of the polygonal lamina, and hence gives rise to an isometry-covariant valuation. The line connecting the circumcenter and the centroid of a triangle is called the Euler line. Taking affine combinations of the circumcenter of mass and the center of mass, one obtains an Euler line of a polygon. The construction of the circumcenter of mass extends to simplicial polytopes and to the spherical and hyperbolic geometries.