My original question is rather vague so I'll start with a precise example and then indicate possible generalisations. Given a n-tuple $x=(x_1,\dots,x_n)$ in, say, a square with side-length $1$ in the ...
Let us consider a disk with one labelled point on the boundary and $n$ labelled points in the interior. Let T be a triangulation of the whole disk with vertices on the labelled points such that T ...
Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equalities between Distance Sums or Differences
Given 4 points $A$, $B$, $C$ and $D$ in general position in the euclidean plane, is it possible to determine from the 6 distances $AB$, $BC$, $CD$, $AD$, $AC$ and, $BD$ alone, whether every point is a ...
A friend and I were reading up on the classification of compact surfaces when we realized that the minimal number of triangles in a triangulation of the sphere, torus, and projective plane are 4 ...