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Let $U$ be an open, bounded and convex set in $\mathbb{R} ^n$. Since $\partial U$ is a rectifiable set it follows that up to a set of $H^{n-1}$-measure zero $\partial U$ is contained in a countable ...

Ref: https://en.wikipedia.org/wiki/Cardioid Earlier posts with similar questions: Smallest 3-ellipses that contain triangles and Curves of constant width that contain triangles Questions: Given any ...

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 ...

Let $p$ and $q$ be positive real numbers with $p \leq q$. Suppose that $H(p,q)$ is the class of all convex arcs $c$ in the Cartesian $x-y$ plane which satisfy the following conditions: (1)The $y$-...