Ferenc Fodor: Minimal area circumscribed quadrangles

One of the classical problems in discrete geometry is the approximation of convex shapes by circumscribed polygons of minimal area. In the talk, we show that for every convex disk $K$, there exists a quadrilateral circumscribed about it whose area is less than $(1−2.6×10^{−7})\sqrt 2$ times the area of $K$. With this, we (slightly) improve the result of W. Kuperberg (2008).

Joint work with Florian Grunbacher (TU Munich).