Imagine the 'Bishop' chess piece. The four directions that it can move can be called 'diagonal'.

Similarly the 'Castle' moves in the horizontal and vertical directions. Is there a single word that describes this movement?


The rook in chess moves orthogonally.

This term is not used often (unlike diagonally) as more authors seem to prefer to spell things out (i.e., horizontally and vertically) to prevent being misunderstood. Still, it can be traced in many chess manuals, such as this one (cf. Basic play section, p. 2).

Orthogonal literally means "along angles", while diagonal means "across angles", where the word angle needs to be understood as "the right angle".

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  • Is it really so? Doesn't orthogonally mean to move at a right angle to something? But the rook only moves straight in one direction. – Martin Peters Sep 8 '15 at 7:49
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    @MartinPeters Orthogonal is quite often used the way you propose (i.e., orthogonal to something), often to mean independent. That's fine, there is however no reason to insist on exclusively this usage. – anemone Sep 8 '15 at 7:58
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    @aquirdturtle: the bishop's two directions of movement are orthogonal to each other, but diagonal to the rows and columns of the chessboard. Both "orthogonal" and "diagonal" require a reference to have unambiguous meaning, right? – herisson Sep 8 '15 at 8:45
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    I down-voted this. Orthogonal does not imply horizontal and vertical movement. Orthogonal implies that one movement is at a right angle with respect to the other. Horizontal and diagonal movements are thus always orthogonal, but two diagonal movements can also be orthogonal to each other. In fact, the two diagonal movements in chess are orthogonal to each other. The fact that a book on chess assumes a one-way usage of the word does not change its definition. That is a fallacy. – JJM Driessen Sep 8 '15 at 9:24
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    @JJMDriessen Thanks for your message. I really appreciate you left a note with your downvote. You will perhaps do me the favour of visiting en.wikipedia.org/wiki/Hippogonal or en.wikipedia.org/wiki/Fairy_chess_piece#Notations for further reference for the term I am proposing. – anemone Sep 8 '15 at 9:34

How about translation (in the mathematical sense)? i.e. both types of movements are examples of translations of the chess pieces

EDIT: oh excluding the diagonal. Ignore me XD

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  • translation would include diagonal movement however – Aequitas Sep 8 '15 at 5:25
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    What do you think of "edge parallel"? – deadrat Sep 8 '15 at 6:41
  • Oh I missed that it was excluding the diagonal T.T – aquirdturtle Sep 8 '15 at 8:31
  • If you've made a mistake, that's fine. You can delete your own answer and leave a comment under the question with this information. – herisson Sep 8 '15 at 9:37

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