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Tuesday, August 20, 2019

How to Mow Your Lawn Using Math | Science - Popular Mechanics

We came up with the calculations, says Dave Linkletter, Ph.D. candidate in Pure Mathematics at the University of Nevada, Las Vegas.

 Photo: Remus Kotsel/Getty Images
Dedicating years of schooling to pursue higher math degrees may help solve certain problems, but does it make any difference for something as simple as cutting your grass? To find out, I spent the week discussing the mathematics of lawn mowing with my colleagues at the University of Nevada, Las Vegas.

Our thoughts generally split into two directions: If your lawn is simple enough, then you can do some fairly specific calculations to figure out the most efficient way to mow it. But if your lawn is weird enough, it might resemble a famous mathematical allegory.

So first you have to ask the question, “What is the topology of my lawn?” Topology is a branch of math that’s only officially existed for about a century. Some mathematicians call it “wiggly geometry” or “geometry without measuring.” Topology studies how regions and surfaces are similar or different, but not in terms of measurements like in geometry.

You can remember it like this: “What’s the volume of a sphere?” is a geometry question. “What’s the difference between a sphere and a donut?” is a topology question...

If you need to mow a sprawling lawn, it might translate into a fun little Graph Theory problem. But if you’ve been mowing it for years, you probably already have the hang on mowing it efficiently. You don’t need advanced math to solve this problem—maybe just to talk about it more abstractly.