All Questions

Is it true that for any given closed Jordan curve of $C \subset \mathbb{R}^2$ there is a dense subset $A$ such that for every point $p\in A$ we have the following property: If we rotate $C$ around $p$...

Is it true that there does not exist a closed convex plane curve containing an infinite number of segments, belonging to distinct lines each?

I am currently trying to find a way to define some notion of "roundness" for subtours in graphs and that definition should only be based on the comparing (sums of) edge length and on the order in ...

Assume that $\gamma$ is a convex curve which is symmetric with respect to two orthogonal lines (the ellipse is such a curve). I want to know if there exists a $(l,L)$-bi-Lipschitz mapping of the unit ...