5 citations · 14 across the 20 of their papers we have counts for
Showing math.MGShow all
3 papers · 1 filter
math.MG2023
Geodesic complexity of a cube
Donald M. Davis
The topological (resp. geodesic) complexity of a topological (resp. metric) space is roughly the smallest number of continuous rules required to choose paths (resp. shortest paths)…
math.MG2023
Geodesic complexity of a tetrahedron
Donald M. Davis
We prove that the geodesic complexity of a regular tetrahedron exceeds its topological complexity by 1 or 2. The proof involves a careful analysis of minimal geodesics on the tetra…
math.MG2023
Isomorphism classes of cut loci for a cube
Donald M Davis, Manyi Guo
We prove that a face of a cube can be optimally partitioned into connected 193 sets on which the cut locus, or ridge tree, is constant up to isomorphism as a labeled graph. These a…