Mathematical Pasta

Geek mom author Helene McLaughlin reviews this great geeky book about the mathematics of 92 (!!) different kinds of pasta [hat tip to Tim Chase]:

 

When mixing flour, egg, salt and water to make pasta, I’d guess the only math you consider is how many minutes you have left before the kids will be begging for dinner. I’d guess that you never really contemplated the mathematical beauty of that rigatoni or cavatappi that you are eating. Thats not the way George L. Legendre eats pasta.

In an effort to bring order to the possible chaos of cooking, George L. Legendre takes cooking geek to the next level with his unique book, “Pasta by Design“. Legendre takes 92 of the most familiar types of pasta, categorizes them, determines the complex mathematical equation describing the shape and shows us incredibly intricate computer models for each type of pasta.

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Stellated Icosahedron

I’ve been motivated by George Hart and Zachary Abel to make my own mathematical sculpture with found objects :-). A few former students dropped by to visit me this afternoon and I put them to work making this (they had no where to be, right!?):

A cardboard stellated icosahedron

It’s a stellated icosahedron, made out of these little triangular pyramids. I did not make the pyramids, they came to me this way. Can you guess what their original purpose was?

Pop quiz: What do you think this is??

My wife and I redid our kitchen a few years ago, and I saved twenty of these from (did you guess it yet?) the packaging our cabinets came in. For each cabinet, there are 8 of these keeping the corners safe. The construction process was pretty straight forward, but here are some photos documenting the event.

Construction begins

Every vertex looks like this on the inside.

Almost done!

The last piece goes on.

Here are some more views of the icosahedron. The icosahedron has a symmetry group of size 60.

There are 15 pairs of opposite edges, each with 2-fold symmetry (for a total of 15 orientations, not counting the identity)

There are 10 pairs of opposite faces, each with 3-fold symmetry (for a total of 20 orientations, not counting the identity)

There are 6 pairs of opposite vertices, each with 5-fold symmetry (for a total of 24 orientations, not counting the identity)

So (1 identity) + (15 edge symmetries) + (20 face symmetries) + (24 vertex symmetries) = 60 total orientations.

Now I just need to find a large enough Christmas tree upon which to put this giant star!

Binder clips!

While daughter Vi Hart is off making crazy videos, including this one she posted today, father George Hart  points us to these incredible scupltures with binder clips, by Zachary Abel. (George Hart is also a mathematical scupltor.) Check out this incredible binder clip sculpture by Zachary, a piece called “Impenetraball”:

He has three sculptures with binder clips, and I thought I’d try my hand at making his simplest one, called “Stressful.”

After doing that, I have a HUGE appreciation for his larger binder clip sculptures. This was not easy to make!