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If you've read many of my other posts, it's probably become obvious that I enjoy spatial reasoning.  It's fun because it involves creating images in your head and knowing how things work together.

One of my favorite childhood toys was this set called Gearopolis.  It was made by Discovery Toys, and it only seems to be available used now.  But all is not lost for fellow gear-lovers who want to play with a toy like this.  Gear Tech is a similar set (and it even includes belts to connect gears!), and it's available from Amazon.com.

Now, one of the things I like about spatial reasoning is figuring out how systems work before testing them.  So let's play that game with my gear setup.

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If the yellow gear with the handle turns counter-clockwise (as the arrow shows), which way will this green gear turn?

Got it?

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Okay, let's try another one.  If we once again turn the yellow gear counter-clockwise, which way will this big purple gear turn?

If you want a real challenge, think about how fast each gear turns.  If I turn the yellow gear at a constant rate, which will turn faster, the green gear or the big purple one?  Or will they be the same?  Will they be faster or slower than the gear with the handle?

Have you figured it all out?  Now you can watch this video to see the gears in motion:



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    Kelly Patton has somehow completed 20 years of formal mathematical education with her love of math intact.  She wishes every person were so lucky, so that's why she writes this blog.