Artie, please consider the pole problem. You know, we’re on a walk you go on one side of the pole I go on the other then we have to unravel. Since, “make sure you’re on the same side as me” doesn’t seem to be effective communication, let us try a more rigorous approach. Consider yourself to be a point, D (for Dog), I’ll be point O (for Owner), and let this pole be point P (for pole). Now consider the direction that I am walking we will call this vector v, construct a line perpendicular to vector v which contains point P and call this line l. Now find the intersection of the line that contains O and is parallel to vector v and l and call this point Q and construct another point R such that P is between Q and R on l. Consider ray PR, do not allow point D to coincide with any points contained in ray PR. Follow this simple formula and segment OD (aka “the leash”) will not become entangled.
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