The Mathematics of Lawn Mowing 514
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:Here's a tip... (Score:2, Insightful)
Here's another tip. More of a rhetorical question, actually: what the hell does anybody need a six-acre lawn for? Can you honestly say that it provides you with more enjoyment than, say, a half-acre lawn?
Interesting Story! (Score:4, Insightful)
First, let me say that I do like this type of story. Interesting, thought provoking, nerdy and mathematical in nature.
I will also preface what I am about to say by noting that people are free to make whatever life tradeoffs they want.
At the same time, I really wonder why anyone would want a property that takes three hours just to cut the grass. Life is short, why spend it maintaining a large property. I make low six figures now and could afford a lot more of a house than I have, and even when I upgrade to a nicer neighborhood next year will still way underbuy what the bank wants me to borrow.
If you are stinking rich and want the large property, go ahead... but hire someone to do it for you. Your time is more valuable than the cost of having someone cut your grass. Give some teenager or out of work adult the opportunity to earn some money. That is the real win-win of capitalism.
Finally, the article linked to seems light on the math itself, but seems very descriptive. I don't know that there is a purely mathematical solution to the problem but wonder if genetic algorithms would get you to where you want to be. I also wonder if you have a yard like mine with tree roots all over the place would change the outcome :)
May we suggest ... (Score:4, Insightful)
Re:Here's a tip... (Score:4, Insightful)
Absolutely. A half-acre is barely enough to do any sports-like activities. There's a very good chance that the ball/disc/boomerang/whatever will end up in the neighbor's yard.
At best, it's a pain to go around and get it, and everyone waits while one person has a good run, unbalancing everything.
At worst, you have a cranky neighbor or break something in your neighbor's yard.
So yeah, having a big yard can make a difference.
If all you do is barbecue, then a 1/2 acre yard is more than enough, though.
Re:Interesting Story! (Score:2, Insightful)
Lawn mowing is a job that you can complete on your own that requires no meetings, team discussions or 300 e-mails before the project can even start. thenyou can step back and admire your work, knowing 37 other people will not take credit for it. ;o)
Lawn? (Score:5, Insightful)
Six acres isn't a lawn, it's a field... anyone else get the impression this guy just wanted a reason to say "I have a six acre lawn"?
Best solution (Score:5, Insightful)
Why the hell do you have 6 acres of grass? Plant some trees for christs sake.
Re:If only Americans had heard of parks. (Score:3, Insightful)
What the fuck do you care how big someone's yard is? Petty little shit.
Re:If only Americans had heard of parks. (Score:5, Insightful)
Well let's see: when I was a little boy we went unsupervised all the time. Violent crime has gone steadily down since I was a kid so why are people are more afraid of letting their kids play unsupervised? Just because we've been trained to fear danger more and more doesn't mean that we or our kids are actually in more danger.
And also, one of the perks of living in a neighbourhood where the families are acquainted with each other is that even when your eyes are not on your kid, other neighbours' eyes are, and if something goes wrong you can count on them to help your kid if needed (with the understanding that you do the same for your neighbour's kid). I'm not a Christian by any means, but "love thy neighbour" was a good practical piece of advice.
The people using the parks will act much less like assholes if they know each other. This is what community is all about. People behave better to those they know than those they don't know. It's the Golden Rule in action.
As for the condition of your parks, might I suggest a modest tax increase, sufficient to allow the municipality to maintain the parks? And failing that, a neighbourhood park maintenance co-op group?
Using your shitty parks as an excuse not to get to know your neighbours, when getting to know them is the best, cheapest solution to your shitty-park problem betrays a shocking lack of reasoning on your part. And yet you're not stupid (presumably). Have we come so far in our hyper-individualistic culture that we can't even see neighbourliness as a possible solution to our problems? Even the problems that were created by hyper-individualism in the first place?
If only foreigners had a clue about US parks ... (Score:5, Insightful)
Perhaps you should consider that many people outside the US are misinformed regarding life in the US, just as many in the US are misinformed about life outside the US.
Re:If only Americans had heard of parks. (Score:2, Insightful)
This is a standard problem in CAM systems (Score:4, Insightful)
All modern computer-aided machining systems have solvers for this problem. When you tell a CAM system to machine an arbitrary area, it computes a tool path to do the job. Here's MasterCam doing it. [thomasnet.com] Even low-end 2D CAM systems can solve the lawnmower problem. High-end systems can solve much tougher problems, automatically deciding what tool to use, clearing big areas with big tools and finishing up the tight spots with small ones. The most advanced CAM tools can do that in 3D on very complex objects. [youtube.com]