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<P>TonyP, you write:</P> <BLOCKQUOTE>'To try and wrap up my end of this discussion of 'angles dashing from a hex in a plane'. There exists a usage convention (tradition with a group of supporters) for using 'orthogonal' and 'diagonal' to describe some possibly paths on a hex grid. The usage (1) isn't especially apt, since it conflicts in some important ways with the usual meaning of orthogonal and diagonal in both chess and mathematics (especially plane geometry)'</BLOCKQUOTE> <P>I just did a google search on the terms 'chess orthogonal', and page after page was on Chess variants rather than on Chess. I then went to the FIDE rules at the FIDE website and looked at its description of how Rooks moved. It said that Rooks moved along ranks and files, and it made no mention of the word orthogonal. I then searched for the word 'orthogonal' on the page, and the search turned up nothing. As I mentioned earlier, I did not learn the word orthogonal when I learned Chess. Instead, I learned that Rooks move straight, and I didn't learn the word orthogonal until I studied Chess variants. Based on all this, I surmise that the word 'orthogonal' is not commonly used for describing the rules of Chess, and, contrary to what you say, there is no usual meaning of orthogonal in Chess. The word, insofar as it is used in a Chess context, seems to be primarily used in Chess variant contexts.</P> <P>As for the usage of the word in mathematics, I don't see the conflict. Like the statistical usage of orthogonal, which is based on the mathematical usage but not identical with it, the Chess variant usage of orthogonal is also based on the mathematical usage but not identical to it. And this is to be expected. Mathematics is a different field than Chess variants, and it has different concerns.</P> <BLOCKQUOTE>and (2) suggests a 'rightness' (based on the analogy to standard chess) that is misguided, a frequent source of confusion, and somewhat stifling for developing other approaches to hex chess. I therefore feel its a usage ripe for replacement.</BLOCKQUOTE> <P>I disagree with all of this.</P>