Mathochism: Don’t trust the picture

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

Call it a geometry miracle, but I somehow scraped an A on the last test.

It helps that Uchitel told us he made a mistake on one of the problems, so we all got that one right. He blames soon-to-vacation brain, since he was about to jet off to tropical paradise when he composed the test. Well, bless him and his distraction, because it clearly pushed me into an A-.

Not everyone was so lucky. There were quite a few Cs, and even a D or two. There but for the grace of the vacation gods go I.

We continued with circles, and I’m not as clear on the relationships between angles and arcs as I should be. I’m also not seeing where the arcs in question are. Of course, it doesn’t help that diagrams aren’t always clear.

That goes double when you’re doing an indirect proof, where you make an incorrect assumption, and therefore an incorrect diagram, to start.

“Don’t trust the picture!” Uchitel has told us in the past, and continues to tell us now. How I wish I had heeded that advice on the last test, and ignored that second diagonal.

Not trusting the picture is good advice for one’s non-math life. Long before photoshop, we’ve been manipulating pictures to make them look worse, or better. That alleged ghost? Double image. That lovely beach? Too bad the dump right next to it was cropped out.

Many years ago, I did a paper on Spanish artist Francisco Goya. He was unusual for painters of the day, since he refused to correct his subject’s flaws and flatter them.

“Yo pinto lo que veo,” he would say, and this got him in plenty of trouble, particularly with the king. Even so, I bet even Goya’s pictures couldn’t be trusted, since he may very well have painted his subjects more negatively or positively, depending on how he liked them.

But back to math — I’m not sure when our next test is (since we seem to continue off schedule). But I will do my best to be critical of diagrams on it when it happens.

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


One comment

  • One of the tricky things about geometry pictures is that they are actually sequences of pictures. If you want to draw a line perpendicular to another line, the sequence goes like this:

    (1) Draw a line, maybe one inch long, say.

    (2) Draw, with your compass, a circle with one end of the line as the center and the other end on the circle.

    (3) Draw another circle, using the other end of the line as the center.

    (4) Your two circles intersect, once above your line and once below. Connect the two points of intersection.

    So really, this is a four-picture sequence. But a geometry text will only show you the last picture. Thinking of geometry pictures as layers (first this layer, then this other one, etc) really helped me figure out what was going on.

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