A Study of Geometry, a Study of Miscommunication…

All right friends, prepare to get seriously nerded on…

I recently came across an article about a bicycle with a pentagonal front wheel and triangular rear wheel. The writer says that even with these weird shaped wheels, the ride is surprisingly smooth. This made me curious: how can a triangular wheel offer a smooth ride??

The article explains: “That is because the edges of the pentagonal and triangular wheels are not perfectly straight. The sides of the shapes bulge outwards in such a way that the wheels share an important feature with the circle: the diameter across the shapes is the same which ever way that you measure it. ”

This only confused me more. How could the diameter be the same every way you measure it? Wouldn’t that make it a circle?? As I visualized various lines going through the center of the triangle, it seemed obvious that the diameter would not be the same.

Reading further, I learned that this is a special triangle called a “Reuleaux Triangle.” So I did what all curious minded people do in this day and age: I looked it up on Wikipedia

Check it out:

(By the way, couldn’t you just watch this animation all day?)

This gave me a better idea about how the triangle could roll, but I still had no clue how the diameter could be the same no matter how you measure it.

So I decided to get to the root of the problem: I looked up Wikipedia’s entry on diameters.

Ah-Ha! Finally, it became clear: “Diameter” can mean different things. From Wikipedia: “For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. ”

Now I got it. The diameter didn’t have to go through the center. In a circle, which is the only context I had ever used the word, the diameter does by definition go through the center. But in other shapes it does not; it just needs to be the longest distance.

Boy, it felt better than it should have to have been able to figure that out and stop obsessing over it. Like I alluded to at the top of this post, I’m a bit of a nerd…

BUT, this got me thinking. I could not possibly fathom how the original article was correct because I was using a different (or incomplete) definition of “diameter.” It’s amazing how much confusion can be created when two people are using the same word in two different ways.

Have you ever been in a long heated argument with someone only to discover that you were both using different words to argue the same point? Have you ever gotten really mad at something someone said and later found out that you misunderstood them?

Miscommunication is the root of many of our problems, both personally and professionally. The next time you start to get irritated at something someone says or you find yourself going rounds with someone who just doesn’t seem to understand you, take a second and think about the words you are both using. Is it possible that one of you is not using the right word in the right way?

That little second of thought could save you hours of headache. If you don’t, you might be called “obtuse” – and not like the triangle!

P.S. You know what’s freaky? A drill bit in this shape would drill an almost near perfect square! Amazing…

About

By Avish Parashar. As the world's only Motivational Improviser, Avish uses techniques from the world of improv comedy to engage, entertain, and educate audiences on ideas around change, creativity, and motivation. Connect with Avish on Google+

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