Spheres, Gears, and Souvenirs

92GearSphere-20-24-16Welcome to this week’s Math Munch!

Whoa. What is that?

Is that even possible?

This gear sphere and many others are the creations of Paul Nylander. There are 92 gears in this gear sphere. Can you figure out how many there are of each color? Do you notice any familiar shapes in the gears’ layout?

What’s especially neat are the sizes of the gears—how many teeth each gear color has. You can see the ratios in the upper left corner. Paul describes some of the steps he took to find gears sizes that would work together. He wrote a computer program to do some searching. Then he did some precise calculating and some trial and error. And finally he made some choices about which possibilities he liked best. Sounds like doing math to me!

Along the way Paul figured out that the blue gears must have a number of teeth that is a multiple of five, while the yellow ones must have a multiple of three. I think that makes sense, looking at the number of red gears around each one. So much swirly symmetry!

Spiral shadows!

Spiral shadows!

Be sure to check out some of Paul’s other math art while you’re on his site. Plus, you can read about a related gear sphere in this post by mathematician John Baez.

I figured there had to be a good math game that involves gears. I didn’t find quite what I expected, but I did find something I like. It’s a game that’s called—surprise, surprise—Gears! It isn’t an online game, but it’s easy to download.

Can you find the moves to make all the gears point downwards?

Can you find the moves to make all the gears point downwards?

This Wuzzit is in trouble!

Wuzzit Trouble!

And if you’re in the mood for some more gear gaming and you have access to a tablet or smartphone, you should check out Wuzzit Trouble. It’s another free download game, brought to you by “The Math Guy” Keith Devlin. Keith discusses the math ideas behind Wuzzit Trouble in this article on his blog and in this video.


Last up this week, I’d like to share with you some souvenirs. If you went on a math vacation or a math tour, where would you go? One of the great things about math is that you can do it anywhere at all. Still, there are some mathy places in the world that would be especially neat to visit. And I don’t mean a place like the Hilbert Hotel (previously)—although you can get a t-shirt or coffee mug from there if you’d like! The mathematician David Hilbert actually spent much of his career in Göttingen, a town and university in Germany. It’s a place I’d love to visit one day. Carl Gauss lived in Göttingen, and so did Felix Klein and Emmy Noether—and lots more, too. A real math destination!

Lots of math has been inspired by or associated with particular places around the world. Just check out this fascinating list on Wikipedia.

Arctic Circle Theorem

The Arctic Circle Theorem

The Warsaw Circle

The Warsaw Circle

Cairo Pentagonal Tiling

The Cairo Pentagonal Tiling

Did you know that our word souvenir comes from the French word for “memory”? One thing that I like about math is that I don’t have to memorize very much—I can just work things out! But every once in a while, there is something totally arbitrary that I just have to remember. Here’s one memory-helper that has stuck with me for a long time.

May you, like our alligator friend, find some good math to munch on. Bon appetit!

48 responses »

  1. this is an interesting video this might help your younger sibling to learn = less than and greater pretty good idea. maybe do a division or something else.

  2. this video is really clever and unique I love the fact that they used an animal to explain greater than, less than or equal to. it reminds me of first grade when my teacher used Pac man to describe the signs. Pac man would always eat the greater number. I really like this videos its sums up it all up into a really catchy kid song.

  3. This video was really cool when I was younger i remember the alligator. I would of never have thought of this idea. It was very creative!!!

  4. First of all this song is so fun and entertaining the lyrics are so cool . When i was little i remember our teacher taught us that way. when I watched this video it reminded me of how i use to do those type of comparing problems . this song is creative and i love it !

  5. I am very impressed with the math art and alligator song. The gears were also interesting. I tried to count the colors the gears have.

  6. This video is very educational and it helps all ages remember which way the signs are supposed face and how you are supposed to solve the problem. I also think that the song is very fun and catchy.

  7. I like how this video makes everything so simple, instead of using a regular technique it uses a much similar way. A way for all ages to understand and making math fun but educated at the same time.

  8. This video was very creative and a good way to remember how to compare numbers I will show this to my younger siblings and it will hopefully help them in school

  9. This is a very cool way to remember what the greater, least and equal sign mean. And to show how to not get confused by them. This is the way I learned as a child, and it has always helped me because, ‘the alligator always eat the biggest number’.

  10. Memories rolling in! That gator just likes eating numbers that are greater, it even rhymes! I remember in 2nd grade or maybe in 1st grade when my teacher showed me that gator. I learned very quickly that the part that was open on the symbol was the gator about to eat the greater number. Easy and brilliant! I wonder how it came to be.

  11. this video is great because it a good way to remember your compare numbers I say that I will show it to my cuzins and family.

  12. I think it was a cute way of explaining to kids greater and lower numbers.I also like how it explains in the song how to tell which one is greater or lower

  13. I thought the animation on the “Number Gator” video was really clever. It shows different types of learning/teaching aural, visual, verbal and you could make it physical learning by making a chomping dance! I showed my little brothers the song.

  14. When the less and greater than signs were first introduced to me I always thought of them as animals of some sort with a big mouth and this video helps remind me of when i thought of it that way and i hope it helps younger people too

  15. I think I like this video because you remember you numbers i will think I show other people for they could remember this and this video is so cute

  16. i got the wuzzit game on my iphone and im stuck on a level in the botany lab
    and how do u come up with all these really cool stuff

  17. i loved that video, it was so creative and clever! i remember how my teacher showed us that the alligator wanted the bigger number when i was little. it is a great way to explain it to a younger sibling or a class. i wonder what other animations they have that explain any ways to remember other things in math. i wish there was one for negative and positive equations because it would be nice to remember that during a test 😀

  18. I love how you used an alligator to explain greater than, less than, and equal to, This video was very unique and educational. I loved it!!

  19. Very cool concept! The Gears game is a very cool game! The aligator edit was very neat but I couldn’t hear if it had sound. I would assume it was even better. The gears GIF was cool, but how did you get it?

  20. Great video and i learned no matter what the aligator always eats the biggest number and that it cant eat two numbers that are equally the same

  21. this is very cool my brother will love this because one he loves crocodiles plus it will help in school alot more because he needs it great video about the crocodile eats the bigger number and if its the same or equal it cant do anything

  22. I thought that this was a really cool article to be able to read because I thought that it was a computerized picture and as I read I learned that it was an actual invention.

  23. The inequality song was okay. That’s a good way to look at inequalities. It would make it easy for kids that can’t understand inequalities to understand them. The video was helpful.

  24. this video is really clever and unique I love the fact that they used an animal to explain greater than, less than or equal to. it reminds me of first grade when my teacher used Pac man to describe the signs. Pac man would always eat the greater number. I really like this videos its sums up it all up into a really catchy kid song.

  25. The song is such a clever way to remember the greater than/less than signs. I’m sure this is more helpful than just simply drilling it into our minds.

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