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Message: <blockquote data-quote="Ourph" data-source="post: 4105821" data-attributes="member: 20239"><p>I don't think the triangle inequality applies here because the problem only arises when you fail to treat the battlemat as its own self-contained universe, where every measurement is relative to every other measurement.  The problem comes in when you translate non-battlemat measurements from the gameworld onto the battlemat without first converting them.  If a room is square on the battlemat, it would actually be round in the gameworld (i.e. all points on the walls would be equidistant from the center).  However, most gameworld rooms won't be round, they will be square and drawing a square gameworld room on the battlemat, appropriately converted for battlemat geometry, would be cumbersome.  So you're mixing geometries by drawing a square gameworld room as square on the battlemat, and that produces errors.  The triangle inequality presupposes that all measurements of the triangle are based on the game geometry.  However, in the case of the square room, the geometry of the hypotenuse is normalized for the battlemat and the geometry of the other sides of the triangle is normalized to that of the gameworld, which breaks the rules and makes all mathematical models void.</p></blockquote><p></p>