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## Submission + - The Mathematics of Lawn Mowing4

Hugh Pickens writes 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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## The Mathematics of Lawn Mowing

• #### Summarizing the algorithm (Score:2)

Here's how you can think of the algorithm more intuitively... It seems that, according to the algorithm, you start on the outside edge and spiral inward.. and.. if you're about to be cut off from an area (being forced to overlap previously mowed grass to get to it) then you first zigzag over that area, then proceed with the spiral.
• #### for a push mower (Score:2)

For a push mower, i would suggest the fewer number of turns the more efficient. Spiraling gets really silly with a push mower towards the center.

• #### Real-world experience (Score:2)

I have worked in commercial lawn care.

The fastest way to mow anything is to pick a line, and then alternate push/pull along the same line from one side to the other while keeping the chute pointing into the previously cut area.

Turning is a waste of time and energy.

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