I am interested finding the collection of points in the Euclidean space that has the maximal minimal pairwise distance subject to an average norm constraint, that is, how to maximize $min_{i \neq j} |x_i - x_j|$ subject to $\frac{1}{n} \sum_{i=1}^n |x_j|^2 \leq1$ where $\{x_1, \ldots, x_n\} \su...

I posted this on Stack Exchange and got a lot of interest, but no answer. A recent Missouri State problem stated that it is easy to decompose the plane into half-open intervals and asked us to do so with intervals pointing in every direction. That got me trying to decompose the plane into closed...

I'm trying to determine the stabilizer of a line in a plane when acted upon by the group of isometries of the plane. Please note that I'm using the notation found in the Wikipedia article on Euclidean plane isometries. I've identified (and hopefully exhausted) the following isometries that will ...

Suppose that $S_1,\dots,S_n$ is a collection of disjoint shapes in the plane, and let $\mathcal{X}$ denote the set of all $n$-tuples of points $\lbrace x_1,\dots,x_n\rbrace$ such that $x_i\in S_i$ for each $i$. For any such tuple $X = \lbrace x_1,\dots,x_n\rbrace$, let $F(X)$ be defined as $F(X...