# Euclidean vs Manhattan vs Chebyshev distance question

• Apr 6th 2010, 07:32 AM
Mastermind
Euclidean vs Manhattan vs Chebyshev distance question
Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance?
Or if AB>AC in one distance norm then AB>AC in any other distance norm?
I will be grateful if you state your source(s).

Thanks from Greece!
• Apr 6th 2010, 12:52 PM
Opalg
Quote:

Originally Posted by Mastermind
Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance?
Or if AB>AC in one distance norm then AB>AC in any other distance norm?
I will be grateful if you state your source(s).

If A = (0,0), B = (6,0) and C = (3,4) then AB>AC in Euclidean distance (because 6>5) but AC>AB in Manhattan distance (because 3+4=7>6).

If A = (0,0), B = (6,8) and C = (9,0) then AB>AC in Euclidean distance (because 10>9) but AC>AB in Chebyshev distance (because max{6,8}=8<9).