A Real World Example of Math Concepts at Work

Obviously, I’m not going for a lot of views with this one.

My teacher said something the other day in passing that struck me as a perfect example of how math can help explain the world.

He said something along the lines that “three points define a plane – that’s why three-legged stools don’t wobble.”

Fortunately he made this statement near the end of class, because that’s all I thought about the rest of class – envisioning a stool and the fact that with a three-legged stool, each leg will always have to be touching the floor. This is not the case with a four legged-stool/chair, as I am sure we’ve all experienced at a restaurant while sitting on a wobbly chair or at a wobbly table.

The math behind this has to do with planes; here’s a great video that explains the concepts of a point, a line, and a plane in an easy to understand manner.

in the case of the three-legged stool, the plane would be the floor. When you place a three-legged stool on the floor (the three legs are like three points), all three legs will be touching the floor. In other words, all three points will be on the plane. Here’s a mathematical explanation for those of you who are still reading.

With a four-legged stool, it is possible that one of the other legs lies on a different plane, thus creating the wobbly situation.

This is one of the reasons why a tripod has three legs; no matter how uneven the floor is, you can always set up the tripod so that all three legs are on the floor, hopefully providing a more stable foundation for a camera that my be resting on it. Here’s some math behind the whole tripod thing.

Now I should point out that just because a three-legged stool doesn’t wobble, that does not necessarily mean it is more stable from a practical perspective. A three legged stool is more likely to tip over if one leans forward to far compared to a four-legged stool. If you are interested in the math behind this, here is a link. By the way, Frank Lloyd Wright once famously designed a three-legged chair, but gave up on it after tumbling out of it.


So there you have it; who knew math could help explain such real world phenomena.

Now the next time you are sitting at a restaurant, and you are sitting on a wobbly chair, you will immediately know that it is not a three legged chair. And if you read any of the links above, you will also know that if you rotate the wobbly 4-legged chair up to 90 degrees in any direction, you will have eliminated the wobble.

The problem is that your chair may now be facing away from the table. But if you’re actually trying this stuff at a restaurant, it may actually be better for all involved that you’re no longer part of the table conversation…

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Jim Borden

Accounting Prof. at Villanova; happily married for 30+ years; father of 3 outstanding young men; vegan; interests: fitness, creativity, education, blogging, social media.

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