some common distances

2 days until TJOI.

Chebyshev distance: max(△x,△y).

Manhattan distance: △x+△y

Euclidean distance: slightly

After changing the coordinates of a point $(x,y)$  to  $(x+y,x-y)$$,\; Manhattan\; distance$$in\; the\; original\; coordinate\; system$$=$  Chebyshev distance in the  $new$  coordinate $system$ becomes ( (x+y)/2 , (xy)/ 2)  , the Chebyshev distance in the original coordinate system = the Manhattan distance in the new coordinate system.

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