Experimenting with different metrics

Non-convex balls

By: Esteban Alfaro Sabogal

Date: 06 august 2023

We are going to draw computationally the points that are a distance < r away from a center or fixed point (c,d) in the plane using SageMath. We are going to experiment with different distances or metrics.

Usual or Euclidean metric (d_u) for c=0, d=0, r=1

Manhattan metric (d_taxi) for c=0, d=0, r=1

                                       

Another balls

This metric ("angular") is non-convex and therefore, it is not topologically equivalent to the usual metric, however both metrics are metrically equivalent. The original formulation of this metrics in Mayorga and Arenas (Lecturas Matemáticas Vol. 24 (2003), 39–51)