Isomorphisms in Five, Parquet Deformations, and POW!

Welcome to this week’s Math Munch!

Here’s a catchy little video. It’s called “Isomorphisms in Five.” Can you figure out why? The note posted below the video says:

An isomorphism is an underlying structure that unites outwardly different mathematical expressions. What underlying structure do these figures share? What other isomorphisms of this structure will you discover?

One of the reasons I LOVE this video is because I really like how the shapes change with the music– which is played in a very interesting time signature. I also love how you can learn a lot about the different growing shape patterns by comparing them. Watch how they grow as the video flips from pattern to pattern. What do you notice? What does the music tell you about their growth?

This video is by a math educator from North Carolina named Stuart Jeckel. The only thing written about him on his “About” page is, “The Art of Math”– so he’s a bit of a mystery! He has three more beautiful videos, all of which present little puzzles for you to solve. Check them out!

(Five-four isn’t a common time-signature for music, but it makes some great pieces. Check out this particularly awesome one. Anyone want to try making a growing shape pattern video to this tune?)

parquet-10

Here is an example of one of my favorite types of geometric patterns– the parquet deformation. To make one, you start with a tessellation. Then you change it- very gradually- until you’ve made a completely different tessellation that’s connected by many tiny steps to the original one.

I love to draw them. It’s challenging, but full of surprises. I never know what it’s going to look like in the end.

2012_10_31-par5Want to try making your own? Check out this site by the professors/architects Tuğrul Yazar and Serkan Uysal. They had one of their classes map out how some different parquet deformations are made. They mostly used computers, but you could follow their instructions by hand, if you like. The image above is a map for the first deformation I showed.

Click on this link to see some awesome deformations made out of tiles. Aren’t they beautiful? And here’s one made by mathematical artist Craig Kaplan. It has a great fractal quality to it:

hilbert_ih62_a

Finally, here’s something I’ve been meaning to share with you for ages! Do you ever crave a good puzzle and aren’t sure where to find one? Look no farther than the Saint Ann’s School Problem of the Week! Each week, math teacher Richard Mann writes a new awesome problem and posts it on this website. Here’s this week’s problem:

For November 26, 2013– In the picture below, find the shaded right triangle marked A, the equilateral triangle marked B and the striped regular hexagon marked C. Six students make the following statements about the picture below: Anne says “I can find an equilateral triangle three times the area of B.”  Ben says I can find an equilateral triangle four times the area of B.” Carol says, “I can find a find a right triangle triple the area of A.” Doug says, “I can find a right triangle five times the area of A.” Eloise says, “I can find a regular hexagon double the area of C.” Frank says, “I can find a regular hexagon three times the area of C.” Which students are undoubtedly mistaken?

30- 60-90

If you solve this week’s problem, send us a solution!

Bon appetit!

9 responses »

  1. That video is pretty cool. It’s entertaining and enthralling at the same time. I think that it’s called Isomorphisms in five because there are 5 different colors beign used.

  2. I really like how the shapes change the music. It’s really interesting. I learned about the different growing shape patterns by comparing them.

  3. I thought that it was so cool that they made this shape(s) by using 3 different kinds of tools. I never knew that you can use those to create beautiful math art.

  4. I like how the pattern grows with the music. But I don’t quite understand what an isomorphism is… if anybody can explain it in a simplified way that would be great!

    • Hi Dawnae! That’s a great question. An isomophism is two or more things that work in the same way, but might look different at first glance. The patterns in the video are isomorphic because they grow in the same way, but look completely different. It’s a lot like saying two things are “equal,” except it applies more to the rules behind them. Does that help?

  5. The pattern really is great and I didn’t even know five four time signature existed. Can a music educator please confirm this time signature’s existence?

  6. Pingback: 2016, ScienTile, and a New Algorithm | Math Munch

  7. Pingback: Near Miss, Curiosa Mathematica, and Poincaré | Math Munch

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