Digital Art, Mastermind, and Pythagoras

Welcome to this week’s Math Munch… on (approximately) Math Munch’s second birthday! Hooray!

Check out this video of mathematical art made by artist Nathan Selikoff:

Cool, right? This piece is called “Beautiful Chaos.” The curves on the screen are made from equations (if you’ve ever graphed a line or a parabola you’ll know what I mean). As the viewer waves her hands around, the equations change– and as the equations change, so do the curves! The result is something that might remind you of the images your computer makes when you play music on it or maybe of something you’d make using a spirograph. All in all, a beautiful and interactive piece of mathematical art.

nathanNathan lives and works as a mathematical artist in Orlando, Florida. As he writes on his website, Nathan uses computer code along with other materials to make art that plays with the mathematical ideas of space, motion, and interaction between objects. To see more of how Nathan does this, check out his giant, interactive marionette or this song that explores the first, second, third, and fourth dimensions:

My school is really lucky to be hosting Nathan this week! We didn’t want any of you, dear readers, to miss out on the excitement, though– so Nathan has kindly agreed to answer your interview questions! Got a question for Nathan? Write it in the box below. He’ll answer seven of your best questions in two weeks!

565px-MastermindNext up, who doesn’t love to play Mastermind? It’s a great combination of logic, patterns, and trickery… but I just hate having to use all those tiny pegs. Well, guess what? You can play it online– no pegs (or opponent) necessary!

As I was playing Mastermind, I started wondering about strategy. What’s the best first guess to make? If I were as smart as a computer, is there a number of guesses in which I could guess any Mastermind code? (This kind of question reminds me of God’s Number and the Rubik’s cube…)

Well, it turns out there is a God’s Number for Mastermind – and that number is five. Just five. If you played perfectly and followed the strategy demonstrated by recreational mathematician Toby Nelson on his website, you could guess ANY Mastermind code in five guesses or less. Toby shares many more interesting questions about Mastermind on his website– I suggest you check it out.

What ARE those irrational numbers, so weird that they get their own bubble??

What ARE those irrational numbers, so weird that they get their own bubble??

Finally, sometime in your mathematical past you may have heard of irrational numbers. These are numbers like the square-root of 2 or pi or e that can’t be written as a fraction– or so people claim. When you start thinking about this claim, however, it may seem strange. There are A LOT of fractions– and none of them equal the square-root of 2? Really? What kind of number is that? It seems like only an irrational person would believe that, at least without proof.

Vi Hart to the rescue! Irrational numbers were encountered long, long ago by the ancient Greek mathematician (and cult leader) Pythagoras– and he didn’t like them much. In this great video, Vi tells all about Pythagoras and the controversial discovery of numbers that aren’t fractions.

If you didn’t follow her explanation of why the square-root of 2 is irrational on your first watch, don’t worry– it’s a complicated idea that’s worth a second (or third or fourth) run-through.

Thanks for a great two years of Math Munch! Bon appetit!

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41 responses »

  1. That was really confusing and the girl talked really fast so my head was just being shot with math cannons but what I do know is that hypthmos or pythagamos or whatever his name was invented the square root of 2 and it was funny how he was scared of beans.

  2. I watched the chaos video, and I don’t understand what you’re doing with your hands. Were you just moving the graphics around?

  3. When I saw the Chaos video I was amazed of the pictures ,but thought how you connected the TV with your hands(did you use a X-box Kinect?). Then I saw the app site and thought that I should download that pretty awesome app.

  4. The chaos video was so beautiful just like the name implied. After I write this comment i’m going to check how to get that app. It is hard for me to think of that as math though.

  5. very weird I get that square thing where it has to be even numbers or its not possible I think. She was talking very fast an if I were pythagamos or whatever his name was I would’ve ran threw the bean field away from the people that were going to kill me. Is the story true or not. Well any way I kind of got a little bit.

    • Hi Jenae! She does talk fast– I had to watch the video a few times before I really understood what she was saying. Sounds like you got a lot out of it on your first watch, though! Maybe give it another go. I don’t know if the bean story is true! I would’ve run through the field, too.

  6. This video about the pythagorean theorum is very interesting but I think the girl talked too fast. I did learn about how the theorum is an infinite formula and it is impossible to find the perfect ratio with the theorum.

    • Hi Asher! She does talk really fast. I had to watch the video more than once to pick up on what she was saying, but I understood little bits more each time. It’s great if you can get the gist of it the first time through! Maybe give it another go. Thanks for the comment!

  7. The Beautiful Chaos video was really cool. So the pattern changes when you move your hands, but I was wondering if it is possible to move them back in to the same place and get the same picture or is it all random and the form just shifts whenever it senses motion. Then I read on the bottom that the lines move because whenever the person moves their hands the equation changes making the lines different. That was interesting to find out.

  8. wow the video was confusing but cool at first I didn’t see the math in the beautiful chaos video and what if you dance instead of just moving your hands would it be cooler or complicate and another question when you move your hands so do the equations right but why doesn’t the equations move when you move your body and hands?

  9. I was sort of confusing because the girl was talking really fast . if you don’t think well I do. but I know you sort of fast forward it. I thin she was talking about what will we have without algerba

  10. I think the chaos video was really cool. I think it was interesting to see how the person was able to move the patterns around without touching and just by moving your hands around.

  11. I watched the video about the beautiful chaos and I thought that it was really pretty and cool. I wonder how you create the four parts to it with one or two hands? Can you create a movie or something with it? Just wondering! :|->

  12. I thought the pythagoras video was very interesting but the girl talked so fast I was not really able to comprehend. Is it possible to find the perfect ratio with the theorum? why didn’t he go around the bean field?

  13. The beautiful Chaos video was so cool although it kind of confused me at the same time. The most amazing part I think is how you don’t have to touch the screen at all. But if you move your hands in the same position twice will the patterns be the same?

  14. I just watched the chaos video and it was very cool. I liked how the hands (is this right) could move the graphics around. I love the designs and how you can use math to create something SOOOO awesome!

  15. The girl in the pythagoras video talked really fast. I was able to understand different parts of the video. The parts that I was able to understand made me interested to learn more.

  16. I just watched the video chaos, I thought it was funny how he was super afraid of beans. There was 1 thing i really didn’t like, that was how fast she talked. and math can be made really fun in this video, and it was cool what he did with his hands.

  17. I also watched the beautiful chaos video and found that one tricky. How did the shapes move and curve. Also how did he create the four parts with just his hands?

  18. I thought the chaos video was so cool because you didn’t have to even touch the screen to make the figure move the other fascinating thing was the colors of the figures and how they moved

  19. I watched the Pythagoras video. It confused me, but I kinda got it. I liked how everything was drawn out so that I could see what was happening. I got to see the story of what happened. That made it interesting to watch. It would have been less confusing if she went slower.

  20. I think its amazing how every curve was made by a mathematical equation, but i have one question how exactly did they put he equation together. Also how did they they do the whole thing

  21. I watched the Chaos video. I loved how he/she moved he/she”s hand to move the colors and how the colors just created a cool motion. At first, I didn’t really get it but when I saw the hands move and I saw the dot move I knew what it was doing. I just thought this video was so awesome because I love art itself and this video was just amazing! I don’t know what else to say except amazing, incredible!

  22. i like the chaos video but it was kinda confusing at first. then when i keep watching the video i soon understand that the colors move by the motion by moving the hand.

  23. I liked how she explained her point, but before that she was getting me really confused with how fast she was talking. oh, and is this a story she made up? or did she hear somewhere? its actually pretty interesting.

  24. I watched beautiful chaos and it was fascinating! I would love to control the colors myself! wouldn’t you guys?! i wonder how that works! i liked the way the colors looked and moved. its so awesome i am speechless! if you know anymore info then plz tell me!

  25. I love this story its very interesting. I can say that it caught my attention. I also love the way that she said facts but also she made joke while telling the story! i love the Pythagoras story best story yet

  26. Its so cool how it looks like she is moving the curves with her hands! Are the arches on a mathematical ratio or is it randomly drawn. The way that the lines get lighter and change color when it overlaps is so cool. I was wondering if you would be able to move the lines back when you put you hands back in the same position? or does it just sense motion?

  27. I watched the Beautiful Chaors and what i found interesting is that you have to do it with hand motion I also wanted to now if it was an app or a online game ?

  28. I thought the Pythagoras video was really interesting and there was a lot cool stuff to learn but the person talked way too fast and it confused me. I noticed that the person who did this video is the same person who did the video we watched in class a while ago, Vi Hart. Also, I liked how Vi Hart tried to make a really complex bit of math funny and easy to understand by doing the video with stop motion Sharpie drawings and the ‘beans’ joke. She made me think that math is not just boring numbers and symbols, it’s sometimes really interesting and fun. I laughed at it and learned a lot about math history too, which I really liked. Also, the complicated ideas would have really confused me but Vi Hart made it seem simple with her colorful illustrations!

  29. I really like how he turned equations and math into art! It is very creative. The technology used is very intriguing, it’s interesting how different movements of the hands changes the equations and makes the images on the screen move and change colors! I wonder how Nathan Selikoff made this happen – is it a sensor or something like a Wii that makes colors and swirls change? I found it so amazing to see the all of this happening.

  30. So Pythagoras didn’t believe in numbers between numbers? So a guy that was smart for his time ended up being sort of a stubborn person who thought that his theorem was always correct? He thought that what he thought was the logic of numbers?

  31. One more thing about Pythagoras. If he didn’t like beans and stopped at the field, don’t you think he would be happy to stomp on the beans because he didn’t like them!?!

  32. it was really amazing how math can be expressed in such beautiful ways like in that chaos video. The curved lines were created by equations, the only question i have is how long did that take? :O

  33. Pythagoras is plain old crazy. All him and no me. Where’s the public’s place? Are they just hanging out in the back corner like “whatever”?

  34. It’s amazing to see that sometimes it takes a strange mind to discover some of the most fundamental concepts in math. I also thought it was interesting that Pythagoras was able to prove his theorem with out the use of algebra.

  35. I watched the Four Dimensions Orchestra, and find it amazing that even though music is directly related to math, a piece can be siphoned off in a way that makes it directly unique to the listener, in such a structural manner. I had no idea that explicitly mathematical music artists existed until just now. I wonder how the chord structures were built, and in what manner the rhythms are organized, because there must be a pattern.

  36. I heard this story before but i never thought that it can go to Alpha Centuri and back twice. This really made me think about powers of ten and exponents.

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