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Is there a name for a type of grid you might find in Battleship? Where coordinates don't relate to points on a grid but rather the squares themselves?

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Surely you can just make a rule to say that the bottom-left integer coordinate represents the square you want and you are done! – BlackAdder Jul 2 '13 at 16:02
I don't really see this as a Mathematics question. But maybe you want an "array"? – Willie Wong Jul 2 '13 at 16:03
No I am asking about the name/definition of such a coordinate system within a mathematical framework. For instance we normally deal with Cartesian coordinate systems but I am wondering if there is a name for the variant mentioned in the OP – user2367428 Jul 2 '13 at 16:05
up vote 4 down vote accepted

"Grid" is as good a name as any: See Regular Grid in Wikipedia: In particular, see the "related" grid: the Cartesian Grid:

"A Cartesian grid is a special case where the elements are unit squares or unit cubes [cubes in the case of a 3-D grid], and the vertices are integer points." [brackets, bold-face mine].

You could also refer to this sort of "playing field" in a game like battleship as an incidence matrix of sorts: where a cell in the ith row and jth column might be occupied, using "$1$", or not occupied, using "$0$".

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I must be forming some sort of dyslexia! ;-) – Amzoti Jul 3 '13 at 0:40

How about alpha-numeric grid? That the coordinates refer to squares rather than vertices is no big deal. Squares can be identified with vertices in the dual of the square lattice (which is also a square lattice).

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