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Indeed, it's not even the same between pieces! Kings have Chebysev geometry while Rooks have taxicab geometry: https://en.wikipedia.org/wiki/Taxicab_geometry#S
by KK7NIL 10mo ago
Indeed, it's not even the same between pieces!
Kings have Chebysev geometry while Rooks have taxicab geometry: https://en.wikipedia.org/wiki/Taxicab_geometry#See_also https://en.wikipedia.org/wiki/Taxicab_geometry#See_also
It's left as an exercise for the reader to figure out the geometry of the remaining pieces.
- daynthelife 10mo agoRooks don't have taxicab geometry. Their metric space is compact even on an infinite board. I think you're thinking of the wazir: https://en.wikipedia.org/wiki/Wazir_(chess) https://en.wikipedia.org/wiki/Wazir_(chess)
- jibal 10mo agohttps://en.wikipedia.org/wiki/Chebyshev_distance https://en.wikipedia.org/wiki/Chebyshev_distance for kings, but on a clear board the rook distance between any two squares is 1 or 2, whereas with Taxicab it could be as much as 14.