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?"

Re:If only Americans had heard of parks.

[MadMartigan2001]

It's called peace and quite. Some crazy Americans believe that having enough space around you so that you cannot hear or see your neighbours is a good thing. Then, when YOU are ready to interact with people you simply go to some public space and interact. Just because some Americans don't want to live like rats in a city does not make them crazy. Some people don't mind the screaming kid next door, or the barking dog down the street but some do. Also, it's not a question of how much resources each person uses, it's a question of how many people are using them. No amount of conservation will offset unrestrained population growth.

Re:If only Americans had heard of parks.

[m.ducharme]

Junkies and drug dealers can be gotten rid of by families actually using the parks; nobody wants to do a deal or shoot up where there are a dozen respectable folk with cell phones hanging around.

As for the homeless and crazy, maybe it's not such a bad thing to expose your children to these people, even encourage your kids to talk to them; might make your kids wonder why the richest country in the world even has homeless and crazy people wandering around. It might even make them wonder if there's anything they can do about it.