All Questions

It is known (see for example the Wikipedia entry on the Reuleaux triangle) that for every curve of constant width (CCW), the largest inscribed circle and the smallest circumscribed circle are ...

Take a plane curve $\gamma$ and a disk of fixed radius whose center moves along $\gamma$. Suppose that $\gamma$ always cuts the disk in two simply connected regions of equal area. Is it true that $\...

Chakerian proved in this paper that a closed curve of length L in the unit ball in $\mathbb{R}^n$ has total curvature at least L. In this later paper Chakerian gave a simpler proof and noted that ...

Q. Is the circle the only shape that, when rolling inside itself, has a point that draws out a scaled copy of itself? Let $C$ be a simple, closed, smooth curve in the plane. (Likely "smooth" can be ...

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 ...