Math Cats, Frieze Music, and Numbers

Welcome to this week’s Math Munch!

I just ran across a website that’s chock full of cool math applets, links, and craft ideas – and perfect for fulfilling those summer math cravings!  Math Cats was created by teacher and parent Wendy Petti to, as she says on her site, “promote open-ended and playful explorations of important math concepts.”

Math Cats has a number of pages of interesting mathematical things to do, but my favorite is the Math Cats Explore the World page.  Here you’ll find links to cool math games and explorations made by Wendy, such as…

… the Crossing the River puzzle!  In this puzzle, you have to get a goat, a cabbage, and a wolf across a river without any of your passengers eating each other!  And…

… the Encyclogram!  Make beautiful images called harmonograms, spirographs, and lissajous figures with this cool applet.  Wendy explains some of the mathematics behind these images, too. And, one of my favorites…

Scaredy Cats!  If you’ve ever played the game NIM, this game will be very familiar.  Here you play against the computer to chase cats away – but don’t be left with the last cat, or you’ll lose!

These are only a few of the fun activities to try on Math Cats.  If you happen to be a teacher or parent, I recommend that you look at Wendy’s Idea Bank.  Here Wendy has put together a very comprehensive and impressive list of mathematics lessons, activities, and links contributed by many teachers.

Next, Vi Hart has a new video that showcases one of my favorite things in mathematics – the frieze.  A frieze is a pattern that repeats infinitely in one direction, like the footsteps of the person walking in a straight line above.  All frieze patterns have translation symmetry – or symmetry that slides or hops – but some friezes have additional symmetries.  The footsteps above also have glide reflection symmetry – a symmetry that flips along a horizontal line and then slides.  Frieze patterns frequently appear in architecture.  You can read more about frieze patterns here.

Reading about frieze patterns is all well and good – but what if you could listen to them?  What would a translation sound like?  A glide reflection?  The inverse of a frieze pattern?  Vi sings the sounds of frieze patterns in this video.

Do you have your own take on frieze music?  Send us your musical compositions at MathMunchTeam@gmail.com .

Finally, if I were to ask you to name the number directly in the middle of 1 and 9, I bet you’d say 5.  But not everyone would.  What would these strange people say – and why would they also be correct?  Learn about this and some of the history, philosophy, and psychology of numbers – and hear some great stories – in this podcast from Radiolab.  It’s called Numbers.

Bon appetit!

P.S. – Paul made a new Yoshimoto video!  The Mega-Monster Mesh comes alive!  Ack!

P.P.S. – Last week – June 28th, to be exact – was Tau Day.  For more information about Tau Day and tau, check out the last bit of this old Math Munch post.  In honor of the occasion, Vi Hart made this new tau video.  And there’s a remix.

Möbius, Escher, Hart

Happy New Year, and welcome to this week’s Math Munch!

Next week, the Math Munch team will be part of a Mathematical Art seminar, so we are featuring some great art.

Möbius Strip II (Red Ants) | M.C. Escher

Check out the Möbius strip.  It’s a topological space you can make by by putting a twist in a looped strip of paper.  It has the bizarre property of being one-sided!  Here’s a video of someone making it, but the music is pretty strange.  I found some Möbius info on an amazing math website called Cut The Knot.  Click herehere and here for three different Möbius pages.

Möbius Strip I | M.C. Escher

M.C. Escher popularized the Möbius strip by featuring them in his famous and mathematical prints.  The picture to the right gives you some idea what happens if you cut a Möbius strip in half.  You could give that a try.

If you look at these pictures, you’ll see why mathematicians love Escher’s art so much.  Escher liked to play with the impossible in his art, but several mathematicians have made his dreams reality.  Take a look at this site called Escher For Real.  If you liked that, check out the sequel, Beyond Escher for Real.

And of course, Vi Hart has done it again, this time with two pieces of Möbius art.  First, Vi bought a DIY (do-it-yourself) music box and wrote a Möbius song!  You can get your own music box here.  She also wrote a Möbius story called Wind and Mr. Ug, and the video is embedded below.

Hoping you have a mathematical week.  Bon appetit!

Balloons, Numbers, and Mathemusic

Welcome to this week’s Math Munch!  We’ve got a full plate for you.

Vi Hart and Balloon Art

Vi Hart is a “recreational mathemusician,” which means she spends a lot of her free time making math, music, and art of all kinds.  She is best known for her “doodling in math class” videos, but her website is full of cool and creative projects.  This week we’re featuring Vi’s balloon art. There are lots of cool pictures and instructions to make your own balloon creations!

Landon Curt Noll

Next up, Landon Curt Noll is a number theorist, computer scientist, and astronomer who does and makes all kinds of cool things.  Three different times, he discovered the largest prime numbers anyone had ever found!  Here’s a link to his list of curious patterns in the prime numbers.  In another venture, Landon wrote a neat little program that tells you the English name of a number.  How do you pronounce 1,213,141,516,171,819?  Give it a try.  I know million, billion, trillion, quadrillion, and quintillion, but what’s after that?  Check it out: Landon lists the first 10,000 powers of ten!

Finally, the connections between math and music often inspire awesome creations.  Here’s a beautiful video by Michael John Blake in which he converts the digits of pi to notes, and we get to hear what pi sounds like.

Here’s a similar video by Lars Erickson who wrote an entire symphony based on the idea.  “The Pi Symphony” also includes the sound of e, another important math number which is about 2.71828…

Bon appetit!