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August 6, 2011 01:05 pm

The Mathematics of Lawn Mowing

Hugh Pickens writes "I enjoy mowing my six-acre lawn with my John Deere 757 zero-turn every week, and over the course of the last five years of mowing I have come up with my own most efficient method of getting the job done which takes me about three hours. While completing my task this morning, I decided after I finished to research the subject to discover if there is a method for determining the most efficient path for mowing, and found that Australians Bunkard Polster and Marty Ross wrote last summer about an elegant mathematical presentation of the problem of mowing an irregularly shaped area as efficiently as possible. First we simplify our golf course mowing problem by covering the course with an array of circles with each circle radius equal to the width of the mower disc. Connecting the centers of the circles produces an equilateral triangular grid, with vertices at the circle centers. Following a path consisting of grid edges, there will necessarily be a fair amount of overlap so the statement of the problem is to minimize the overlap by minimizing the number of vertices that are visited more than once which Polster and Ross say is easily achieved by well-known computer search algorithms. Any other tips from Slashdot readers?"

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