TL;DR
This paper investigates the problem of finding optimal billiard paths in a square for lawn mowing, focusing on covering radius and shortest paths given a fixed blade size.
Contribution
It introduces a method to determine the optimal covering radius and shortest covering path for billiard trajectories in the unit square.
Findings
Calculated the optimal covering radius for given trajectories.
Identified the shortest paths covering the square for fixed blade radii.
Provided a framework for analyzing billiard paths in lawn mowing scenarios.
Abstract
We study the Lawn Mowing Problem restricted to periodic billiard paths in the unit square. Given the combinatorial data of a trajectory, we determine the optimal covering radius, and identify the shortest path that covers the square for any fixed blade radius.
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