Mathochism: Methods of exhaustion

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We’re nearing the end of geometry. Four more lectures, one more test, the final, and it’s all done.

Uchitel is caught up on the syllabus, so the latest class was a review. We’re back on circles, only this time, we’re focusing on circumference and area.

Yes, we have involved pi.

I’ve always found pi to be one of those mystical concepts in math. After all, it’s an irrational repeating decimal, and it repeats to infinity. But before taking this geometry class, I never wondered how pi was discovered, or for that matter, how difficult figuring out the exact area of a circle can be.

It turns out it’s impossible to figure out the exact area of a circle. We can get very, very close, yes — but never exact. This is old knowledge, Uchitel tells us, and was figured out by the Greeks several thousand years ago.

Their method, Uchitel told us, was one of “exhaustion,” as in, try everything until exhausted. He had us try this, and the class puzzled over a way to find the area of a circle without pi for a good 10 minutes before suggesting that putting a many-sided regular polygon into it was the best way.

A polygon has straight sides that can be measured in a way a circle’s curved sides cannot. I get that, but I also wonder — why not just use measuring tape? Why can’t the measuring implement be flexible?

This of course conjures up an image of ancient Greeks running around circular Athenian fields with long swatches of fabric (no doubt woven by their young and unappreciated wives) trying to figure out the perimeter. That doesn’t strike me as very dignified. It probably didn’t help that the Spartans (widely known as the jocks of Greece) were likely making fun of them the whole time.

At any rate, I have a new appreciation for measuring things in general. Our experiment with circles inspired Uchitel to go back to calculus, and explain to us how geometry provides a foundation for measuring the tough stuff, like arcs and curves. It was almost like he was trying to justify the importance of the course to us, and I admit I was once one of the skeptical ones.

But back to methods of exhaustion — yesterday, I signed up for pre-calculus. It is a six-week course, two-and-a-half hours, five days a week. If that doesn’t sound intense enough, my class meets first thing in the morning. And I mean FIRST THING. I’m exhausted just thinking about it, but chose that torturous section for a number of practical reasons I will not go into now.

I get the feeling that this next class will definitely live up to its mathochism brand. Time to get caught up on my sleep now.

All text copyrighted by A.K. Whitney, and cannot be used without permission.


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