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That’s The Wrong Math Formula

March 30, 2021

A few months ago I talked about a mistake that my 6th grade teacher made. (A Response To My 6th Grade Teacher.) Even though it was decades, I still remember a lot of what Mr Michalek taught me. Of course, the parts I remember best were when he was wrong.

In 6th grade the teacher covers all the topics. The next year, in 7th grade, we got to move between classes. But, 6th grade was still like elementary school. The teacher has to know a little history, a little English, and of course a little math. I don’t think Math was Mr Michalek’s first love.

The problem with 6th graders, are they are just starting to aquire a few critical thinking skills. And they are obnoxious. I know. I was an obnoxious 6th grader. I suppose I have some excuse. I had what you might describe as a tumultuous childhood. We moved a lot. You are thinking you know what that means. You don’t. I went to 5 different schools in the 5th grade. I finally ended up at Lakes Elementary.

Finally, I had stability, although I didn’t know it at the time. We lived in that house for the next 7 years. I finished up 5th grade at Lakes and then moved on with my classmates to Nisqually Middle School, where they had grades 6, 7 and 8. Eventually I went to Timberline High School where I despite my best efforts, I managed to graduate.

But, back to 6th grade. We were having a math lesson. Mr Michalek informed us that given a set circumference, the volume inside the circumference is always the same. Maybe you are good at math and you are now thinking, “Well, that’s not right!”

You’re right, of course, but as a 6th grader, I didn’t understand how to calculate area. Well, that’s not exactly true. I knew that you could multiple the width times the length and you’d get the area. But, what if I cut the width in half? No, that won’t work. The length doubles and the area is the same.

I didn’t believe Mr Michalek. I couldn’t prove it but it didn’t feel right. I just couldn’t prove it. You probably can. And today, it would be simple. The area of a circle is pi times the radius squared. And today I also understand that the maximum area for a given circumference is a circle. It’s one reason that barrels are round.

But as a 12 year old we hadn’t covered circles. At least not to that level. But, I kept thinking about it. All weekend I went over the problem in my mind. And finally I came up with a simple, non-mathematical solution. Had I lived in Utah instead of Washington, I would have figured it out sooner, I think.

I mentioned I was an obnoxious kid, right? Well, on Monday, I raised my hand eagerly in class,

Mr. Michalek!

Yes, Rodney.

Last week you told us that for a given border the area inside was always the same.

That’s right.

You’re wrong.

Oh really? Care to show the class?

I proudly walked to the blackboard. (Okay, it was probably more cocky than proud.) It turns out that Utah was the solution to my problem. Draw a square. Now, fold down one corner. The length of the circumference stays the same, but you have just “removed” some of your area.

That’s two you got wrong, Mr Michalek. And probably thousands that you got right.

Stay safe

Rodney M Bliss is an author, columnist and IT Consultant. His blog updates every weekday. He lives in Pleasant Grove, UT with his lovely wife, thirteen children and grandchildren.

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