Happy Right Triangle Day! Today, on 9/15/12, we celebrate a favorite triangle: the 9-12-15 right triangle.
We know this triangle is right because the side lengths satisfy the Pythagorean Theorem.
This isn’t the only Right Triangle Day this year. And these two right triangles work together to form one of my all-time favorite triangles!
A lot of nervous energy was building up while I was waiting in the wings at the 2012 TEDxNYED conference.
Luckily, I found some polygons to play around with, so I converted my anxiety into mathematical art.
This is an great website full of galleries of mathematical images:
http://www.josleys.com/galleries.php
There hundreds of beautiful images in many categories, like fractals, knots, spirals, and tesselations.
There’s even a gallery inspired by the techniques of M.C. Escher!
I consider myself an expert arranger of things. I enjoy rearranging storage space, packing things away, and helping people fill up moving trucks. It’s a way to apply geometry and optimization techniques, two of my favorite things.
In general, the packing problem entails trying to find the most efficient way to pack a certain kind (or kinds) of object into a certain fixed space. Packing problems are, generally speaking, very challenging because every packing problem is unique. There isn’t a good, efficient procedure that solves them all.
Here is yet another example of problems with packing problems. After shedding a bunch of CD cases, I thought I’d try to pack them up in a box. Here was my first attempt.
I got 49 CDs in the box, but there was a bit of unused space left over. I couldn’t fit a CD into that unused space, but I thought maybe I could rearrange everything to make some of that space usable.
So I tried again.
The number of CDs in this new arrangement differed by one. While I can compare which of these packings is more efficient, the problem is comparing all possible packings! There are a lot of options to consider.
As useless as they are, I ended up having a lot of fun with these CD cases. I made some parallelepipeds with them and used them to demonstrate Cavalieri’s Principle!
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This is great website from Joseph O’Rourke, author of “How to Fold It: The Mathematics of Linkages, Origami,and Polyhedra” .
The website has several videosand cool animations that demonstrate some of the basic ideas in mathematical folding, like the one-cut problem, the map puzzle, and folding polygons into convex polyhedra.
There are also a few folding patterns available for download, just in case you’d like to produce a turtle with one cut!
And for more resources on math and origami, check out my fun with folding page!
