Nerding Out

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What better way to spend a miserable weather day than playing with math experiments. I’ve been totally nerding out for the last while. Remember Spirograph? Remember trying to keep those gears lined up!!! Some of the patterns get quite complicated and it is frustrating when you mess it up just as you are about to finish the last few turns.
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As I started to fiddle with them I began to realize this could be a lot of fun to try to figure out mathematically. (Note ** Although I am a math keener I have no education in mathematics past high school. I’ve just loved teaching it for years and years and got hooked on experiments and reading about math oddities.) Turns out there is some neat math in Spirograph. If you find the Lowest Common Multiple between the number of teeth on the outside gear and the number of teeth on the inside gear you can predict all kinds of things about the pattern you’ll get. I charted ALL of the patterns for each gear from the biggest to ‘almost’ the littlest. Then I figured out the LCM’s and predicted what I’d get with the rest. It worked!
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Now … I’m pretty sure there is a relationship between the hole in the gear you use to trace and something related to the measures of the ensuing circle you are using. Believe it or not I’m really crazy enough to keep on going to finish up the last section of gears … and then I’ll have a blast looking for all the mathematical relationships I can find with the gear ratios. Loving this time to learn what I want! 😉 Hope you were a little more enthused with your day than Teddy was with my demands that he stay off my charts!

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