A formula for f(K,L) (and proof thereof) is given in this paper: (I have a copy if anyone is interested. --Edwin) Pattern Recognition Letters 7 (1988) 215 226 April [988 North-Holland Knight's distance in digital geometry P.P. DAS and B.N. CHATTERJI Using the knight's moves in the game of chess, the knight's distance is defined for the digital plane. The functional form is presented. An algorithm is given for tracing a minimal knight's path. The properties of some related topological entities are given. Finally the Knight's transform is defined On Sat, Apr 12, 2014 at 9:54 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Let f(K,L) := the smallest number of knight moves {(+-2,+-1),(+-1,+-2)} it takes to get from square (0,0) to square (K,L) on an infinite chessboard.
WLOG assume K,L > 0.
Then find an explicit way to express f(K,L), and prove its correctness.
--Dan
On Apr 12, 2014, at 6:18 AM, David Wilson <davidwwilson@comcast.net> wrote:
I've kind of lost track of this thread. What exactly is the "Knight distance formula" to be proved?
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