The Geometry of Putting on a Planar Surface

TL;DR

This paper analyzes the geometric properties of putting on a planar surface, revealing a universal target point structure that can improve putting accuracy by considering multiple potential target lines.

Contribution

It introduces a geometric model of putting that identifies a universal target point structure, providing a new methodology for reading putts based on shared target points.

Findings

Target points form a diamond-shaped structure centered above the hole.

A universal curve approximates the target diamond for various putt lengths and surface conditions.

Using shared target points can enhance putting accuracy.

Abstract

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.