Geodesic complexity of a tetrahedron
Donald M. Davis – GJM, Volume 8, Issue 2 (2023), 15-22.
- Post by: administration
- janvier 6, 2024
- Comments off
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) between any points of the space. 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 shortest paths on the tetrahedron.
Categories: Issue2
Milestones:
Received: July 25, 2023
Accepted: October 30, 2023
Revised: November 03, 2023
Authors:
Donald M. DavisDepartment of Mathematics, Lehigh University,
Bethlehem, PA 18015, USA