Category: Math

  • You never know when someone will do something cool with your open-source project

    So, a little bit of backstory: about 5 years ago, I became very interested in triangle centers for a while, because I thought they were going to solve my problems with the square-peg theorem (they didn’t). Triangle centers are various special points that you can define for a triangle in the plane: say, the center…

  • How “building a fence around FERPA” is hurting your college education

    So I just got back from the TPSE Math (Transforming Post-Secondary Education (in Math)) meeting in Austin this weekend. First off, it was in fact really cool, with a ton of interesting people with lots of interesting things to say about the future of math teaching in college. The experience got me in the mood to write…

  • Why are we doing this in Math class again?

    I just read a very interesting answer on Quora about whether we have too much math and science education in the U.S. school system. You can read the whole thing at the link, but it made a pretty good discussion about why I’m shifting my calculus class to do some much larger, integrative labs (with…

  • Image Compression Competition 2014

    Every year that I teach the numerical analysis sequence, we end the year with a project on image compression. This year, the students used a technique called Principal Component Analysis (PCA) to sort though large datasets of images, looking for a common structure in the image data. Once they discovered the structure, they could use…

  • 3d printable tight knots!

    I just finished uploading a large collection of my tight knots and links to Thingiverse, where they can be downloaded for 3d printing or sent to Shapeways or another service. The ever-awesome Laura Taalman did a bunch of these over the summer, and I was so inspired that ever since I’ve wanted to put the…

  • Victory! (Of a sort)

    So I’ve been working for a few days on understanding LuxRender, which if you’ve never seen it is a quite impressive global illumination renderer. I’ve been trying to piece together a Mathematica interface which will allow me to take quick snaps of tubes, knots, random polygons and the like and been completely befuddled. Aside from…

  • Image for PNAS Special Topology Issue

    I just finished making a small contribution to this image (hopefully to appear on the cover of the Proceedings of the National Academy of Sciences) built by Tammy Cantarella and Aaron Abrams. The structure illustrates some of Aaron’s research on Dehn functions. Aaron’s work is way deeper than this example, but the example is still…

  • Solving Mazes by Coloring

    Most people know that you can always solve a maze (eventually) by turning left. Here’s a more visual solution to the maze problem which I developed for a elementary school class at Waseca Montessori School in Athens, Georgia. Instead of thinking about the maze, think about the walls of the maze: if there’s a path…

  • Fold And Cut Puzzles

    Erik Demaine, Marty Demaine, and Anna Lubiw proved the following amazing thing a few years ago: You can fold a piece of paper so that ANY shape with straight edges can be cut out of the paper with a single cut. see Erik’s page on Fold-And-Cut problems to read more about the history of this fact. (Did…

  • Folding movies illustrate theorem about flat surfaces

    I learned the really interesting theorem from Joe Fu that a flat polyhedral surface always has the property that the spherical polygon enclosed by all the surface normals at a vertex always encloses area zero. As a favor to Joe, I made some neat Mathematica movies showing the folding process taking a flat sheet with…