# Context and Notation

While other spaces have been considered, most of the theory concerns subsets of $n$-dimensional Euclidean space R$^n$ and this is the setting here. The origin in R$^n$ is denoted by $o$ and $S^{n-1}$ is the unit sphere. If $x$ ∈ R$^n\setminus\{o\}$, then $x^{\perp}$ is the hyperplane through the origin orthogonal to $x$. If $S$ is a subspace (always meaning linear subspace) of R$^n$ and $E$ is a subset of R$^n$, then $E|S$ is the projection (always meaning orthogonal projection) of $E$ onto $S$.