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Euclidian Green Reading, Newtonian Putting

Rule one: do not get fooled: like a pond, the horizon or standing people, a pending putter gives you the direction of gravity. But the popular belief that position of ball and hole relative to the hanging putter gives you a clue to the curve of your line is geometric superstition. In the picture, you see that, irrespective of whether your putting line is straight or curved, you can always hold your freely hanging putter such that putter, ball, and hole are all on one and the same flat vertical plane (black shaded).

What is your putting line? You normally have a mathematically infinite number, but they all require different speeds. Some options from low to high speed: 1 (where you have a speed margin, for the others you don't), then 3, then 4, and the required speed for line 2 is close to that of 4. Your preference is likely the lowest speed line 1. If line 1 is unfeasible you may think of line 3. If you fear a wobbly trajectory you might wish to reduce error by increasing speed and shortening the line length, choosing a line somewhat "under" 3.