All Questions

Background The $n$-dimensional Euclidean ball of radius $1/2$ has width $1$ in every direction. Namely, when you consider a pair of parallel tangent hyperplanes in any direction the distance between ...

Is it possible to find four norms $\| \cdot\|_k$ $( 1 \leq k \leq 4)$ on the plane such that a three-dimensional normed space containing four subspaces isometric to these normed planes does not exist? ...

The effective radius $er(A)$ of a $n$-solid $A$, is defined by Schramm (see the question by Gil Kalai Volumes of Sets of Constant Width in High Dimensions) to be the radius of the $n$-ball that has ...

Let $b(X)$ be the boundary of any $X$ subset of the plane. Does there exist $A,B$ convex compact sets of the plane, such that $C:=A\setminus B$ is simply connected and not empty, and such that ...