The Geometry of Putting on a Planar Surface

This paper explores the geometry of putting in the limiting case of a planar putting surface. Putts equidistant from the hole originating on an arc spanning \pm30 degrees are shown to share a common target point. Moving around the circle of all equidistant putts, the ensemble of target points map out a small, diamond-shaped structure centered on the fall line directly above the hole. The position and size of this target diamond for any length putt on a putting surface of any grade and speed is reasonably approximated by a single universal curve. This understanding suggests a practical methodology for reading putts. Instead of lining up only the putt-at-hand, the golfer should line up all putts known to share a common target point. This methodology will increase the probability of choosing the correct target line.