Tag Archives: doodling

Noodles, Flowsnake, and Symmetry

Welcome to this week’s Math Munch!

Gemelli, by Sander Huisman

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!

Triangles, Triangles, Triangles!

Welcome to this week’s Math Munch!

Inspired by Vi Hart’s most recent doodling video “Triangle Party!”, this week’s post is all about triangles.

Connie Liu

One of the most amazing things about mathematics is that there are always new discoveries to be made about even the simplest of objects–even triangles!  Check out this article about Connie Liu, a Hawaiian teenager who just last year discovered some new formulas that relate special points of triangles to each other.  Connie has found some new, simple, and interesting ways of describing the triangle inequality – just by sticking with her questions and digging into a particular part of mathematics a little deeper than anyone had before.

Next up, here are some visual perspectives on Pascal’s triangle.  Even folks who are well acquainted with this numerical cascade are likely to find something new to see in these blog posts by Tao Wang.  Tao is a math and computer teacher in NYC.  My favorite visualization is the video that depicts the entries of Pascal’s triangle as blocks that are as tall as their numerical value.

Hat tip to Patrick Honner, a math teacher from Brooklyn, for the Pascal’s triangle visualizations.  Patrick writes a sweet mathematical blog, including a running series of photographs about the math that he sees in the world.  Check out his posts about which of these isosceles triangles is “more equilateral.”

Zooming in on the corner of a Koch snowflake.

Finally, Vi mentions and doodles a Koch snowflake in her video.  This seems timely, what with snowfalls likely just around the corner.  Here are some great images of generalizations of the Koch snowflake by Phil Keenan that he made using computers.

Wow, what a great crop of other blogs for you to explore!

Here is a list of them all:

Math Laoshi by Tao Wang

Math Appreciation by Patrick Honner

Meandering Through Mathematics by Phil Keenan

and of course Vi Hart’s Blog

Stay tuned for more winter-inspired mathematics next week!

Bon appetit!

Circles, Geomagic, and Marble Calculators

Welcome to this week’s Math Munch!

We gave you a taste of some of Vi Hart’s math art last week with her balloon creations.  This week, we’re featuring some of Vi’s doodling in math class art – her Apollonian gaskets!  An Apollonian gasket is a fractal made by drawing a big circle, drawing two or three (or more!) smaller circles inside of it so that they fit snugly, and then filling all of the left-over empty space with smaller and smaller circles.  Here’s the video in which Vi tells how she draws Apollonian gaskets with circles and other shapes (and how she makes other awesome things like an infinitely long caravan of camels fading into the distance).  And here are some more Apollonian gaskets made by filling other shapes with circles from Math Freeze.

Next, you may have seen a magic square before, a number puzzle in which you fill a square grid with numbers so that each row, column, and diagonal have the same sum.  (Play with one here.)  But have you ever seen a geomagic square?

Magic squares have been around for thousands of years, but in 2001, Lee Sallows started thinking about them in a new way.  Lee realized that you could think of the numbers in the square as sticks of particular lengths, and the number being added to as an amount of space you were trying to fill with those sticks.  That led him to try to make magic squares out of things like pentominoes and other polyominoes, butterflies,  and many other shapes!  Aren’t they beautiful?

Finally, what do marbles, binary, and wooden levers have in common?  Mathematical artist, designer, and wood-worker Matthias Wandel built a binary adding machine that uses marbles and wooden gates!  Here’s a video demonstrating how it works:

Matthias doesn’t only build calculators.  Here’s a marble elevator and a machine that you can take apart and reassemble to make a new track.

Bon Appetit!