  Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and
quaternionic spaces are related, respectively, to classical determinantal
varieties of symmetric, general, and skew-symmetric bilinear forms.
  Cayley-Menger varieties arise in the Euclidean case, and have relevance for
mechanical linkages, polygon spaces and rigidity theory.
  Applications include upper bounds for realizations of planar Laman graphs
with prescribed edge-lengths and examples of special Lagrangians in Calabi-Yau
manifolds.
