A circle of radius r for the Chebyshev distance (L∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance. However, this equivalence between L1 and L∞ metrics does not generalise to higher dimensions.
A circle of radius r for the Chebyshev distance (L∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance However this equivalence between L1 and L∞ metrics does not generalise to higher dimensions