# Noodles, Flowsnake, and Symmetry

Welcome to this week’s Math Munch!

Gemelli, by Sander Huisman

How much do you like pasta?  Well, these mathematicians and scientists from around the world like pasta so much that they’ve been studying its shape mathematically!  Check out this New York Times article about Sander Huisman, a graduate student in physics from the Netherlands, and Marco Guarnieri and George L. Legendre, two architects from London, who have all taken up making graphs of and equations for pasta shapes.  Sander posts his pasta-graphs on his blog.  Legendre wrote this book about math and pasta, called Pasta By Design.  Legendre has even invented a new type of pasta, shaped like a Mobius strip (see last week’s Math Munch for lots of cool things with Mobius strips), which he named after his baby daughter, Ioli!

Some of Legendre’s pasta plots

Next, here comes the flowsnake.  Wait – don’t run away!  The flowsnake is not a terrifying monster, despite it’s ominous name.  It is a space-filing curve, meaning that the complete curve covers every single point in a part of two-dimensional space.  So if you were to try to draw a flowsnake on a piece of paper, you wouldn’t be able to see any white when you were done.  It’s named flowsnake because it resembles a snowflake.

The flowsnake curve

 A single piece of the flowsnake curve. Units of flowsnake fit together like puzzle pieces to fill the plane

Finally, check out this awesome online symmetry-sketcher, called Symmetry Artist!  Here, you can make doodles of all kinds and then choose how you want to reflect and rotate them.  Fun!

Bon appetit!

# 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!