*[ht: Tim Chase]*

# Category Archives: Geometry

# 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.

# String Quartet

Reposting this amazing video, without too much comment. It’s visually beautiful and makes me want to try some 3d string constructions myself.

*[ht: Gene Chase]*

# 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!?):

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?

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.

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

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!

# Spheres

# Trapezoid Problem (take 2)

Am I blundering fool? You decide!

It turns out the trapezoid construction I posted earlier today *is* trivial. Thanks to Alexander Bogomolny for pointing out my error. The construction is quite easy (and it does *not* require the height), and I quote Alexander:

No, you do not need the height.

Imagine a trapezoid. Draw a line parallel to a side (not a base) from a vertex not on that side. In principle, there are two such lines. One of these is inside the trapezoid. This line, the other side (the one adjacent to the line) and the difference of the bases form a triangle that could be constructed with straightedge and compass by SSS. Next, extend its base and draw through its apex another base. That’s it.

So I redid my Geogebra Applet and posted it here. It’s not really worth checking out, though, since it’s indistinguishable from my previous applet. (In truth, you can reveal the construction lines and see the slight differences.) But I did it for my own satisfaction, just to get the job done correctly :-). Anyway, three cheers for mathematical elegance, and for Alexander Bogomolny*.

*check out Alexander’s *awesome* blog & site, a true institution in the online math community!