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<P>When I first learned to play Chess as a child, I learned that the Rook moves straight. I did not know the word orthogonal until I began studying Chess variants in more recent years. Because of the definition of straight that I learned in geometry class, straight seemed like an inadequate term for how the Rook moves. After all, the Bishop also moves in a straight line. But the word straight has senses besides the one used in geometry, and there is one common and everyday sense of straight that adequately describes how a Rook moves even on a hexagonal board. Let me now quote from Webster's: 'lying along or holding to a direct or proper course or method.' And let me continue with some related definitions: 'not deviating from an indicated pattern' and 'exhibiting no deviation from what is established or accepted as usual, normal, or proper.' Suppose I live on a curved road, and we are on the road, headed to where I live. And I say to you, 'I live straight down the road.' Would you think me mad because I don't live on a straight road? Would you drive off the road in order to go in a straight line? Or would you understand that you will find my house by continuing down the road? In the same sense that I used straight here, the hexagonal Rook moves straight, and the hexagonal Bishop does not. The geometry of the board defines certain natural paths, and these are what the Rook moves along. In contrast, the Bishop moves along paths that cut across the natural paths of the board. As it happens, the roots of orthogonal allow an interpretation of orthogonal that is synonomous with this sense of straight. So either word may do for describing how a Rook moves.</P> <P>Now let me amend what I was saying about diagonal last night. In <A HREF='http://www.chessvariants.com/misc.dir/coreglossary.html'>A Glossary of Basic Chess Variant Terms</a>, John William Brown provides the term 'radial move,' which he defines as a move that is either diagonal or orthogonal. In looking up radial in the dictionary, I don't find any mention of diagonal or orthogonal directions, but I do find that it can describe lines originating from a common center. So, the idea behind this technical sense of radial is that diagonal and orthogonal lines of movement converge at a common center. So let's now apply this concept to movement along a Chess board. A radial line of movement would be one that passes through the center of every space it connects. This distinguishes it from an angular line of movement, which doesn't always pass through the center of connected spaces.</P> <P>Now, as Brown was defining the term, it includes both diagonal and orthogonal movement. It is now simple to distinguish between these. An orthogonal line of movement is a radial line of movement that never passes through corners. A diagonal line of movement is a radial line of movement that does pass through corners.</P>