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?"

Comments

If only Americans had heard of parks.

[Anonymous Coward]

This is a fantastic example of how Americans take a simple problem and absolutely fuck up the solution.

So these Americans want to partake in some outdoor activity that requires a bit of open grass. Their solution? Buy a 6 acre lawn, pay property taxes on this land, buy a lawnmower, buy fuel for the lawnmower, buy fertilizer for the lawn, and waste hours each week mowing the lawn. Even if they pay somebody to maintain it for them, it's still a huge waste of money, time, and effort.

What do people in sensible countries do? They build parks, and everybody in the vicinity contributes a small amount of money towards its upkeep, without the burden falling directly on their shoulders. They can go use it whenever they want, and such parks are large enough that thousands of people can partake in all sorts of sports or other activities at the same time, from barbecuing, to playing catch, to even playing golf, without interfering with one another.

Oh, wait. Parks are probably too "socialist" at best, or "communist" at worst, for most Americans.

Re:If only Americans had heard of parks.

[Anonymous Coward]

@AC and Monsieur Douche Army:

Ah, there's that European elitism I remember so well! It must be coming out of the woodwork in response to all this "credit rating downgrade" hogwash, as if we couldn't cure 100% of our deficit problems OVERNIGHT, and our debt problems IN A DECADE by making you pasty fuckers handle your own security!

If you'll excuse me, I'll just call all our boys home from Germany. I'm sure y'all won't mind the occasional German or even Russian houseguest you might be called upon to lodge involuntarily. And God knows your women are longing for some of that Sausage with Sauerkraut they used to get so often.

Enjoy the schadenfreude while it lasts, Eurotards. I'm sure the collapse of your "single currency" will go along just *peacefully*, and we *won't* have to come running to your rescue yet again. Yeah, that Euro lasted a long time didn't it? We've had a single currency for, oh, two hundred years, and you couldn't manage two decades!

And I hear you: "America's debt problems are really all about the oil wars". Yep, I agree. Plenty of us do. And we're trying to do something about it.

But just remember, Eurokids: we DO have energy alternatives, and we kinda invented high-tech and green-tech, so we'll be sure to offer you the "friend" discount when your "petrol" supplies are cut off by the Bear, the Dragon, and the Arabs....the "Friend That's There When They Need Us Discount", that is.