I am wondering when can the Taxicab metric be less than the Euclidean metric.
I am aware that usually the Taxicab metric > Euclidean metric and it would be the same if the 2 set of points are in the same vertical or horizontal line. But how can we introduce a constant C such that Taxicab metric < C * Euclidean metric.
Perhaps some reasoning for why C was chosen would be great.
Thank you.