All Questions

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 $\...

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 ...

I am trying to find a large subset of piecewise-differentiable plane curves of finite length (subsets of $\mathbb{R}^2$) with the following property: For any pair $\gamma_1, \gamma_2$ of curves in ...

Let $\textit{F}$ be the family of $C^1$ curves in $\mathbb{R}^2$ of fixed length $\bar{l}$ and fixed tangent's turning angle $\bar{k}$. What are the curves of positive curvature in $\textit{F}$ ...

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 ...