Suddenly Tic-Tac-Toe isn’t boring!

They were laughing and playing Tic-Tac-Toe. At 7:45am, no less. So I wandered into the math center to see just what was so exciting to the handful of math majors gathered around the computer before their Algebra class.

It turns out they were playing Tic Tac Toe on a Klein Bottle. Several of our students went to the Hudson River Undergraduate Mathematics Conference this past weekend, and the keynote speaker, Jeff Weeks (a freelance mathematician) had presented several geometry games. The students were playing Torus Games, in which traditional games like tic tac toe or billiards are played on a torus or on a Klein bottle. And I was jealous, because suddenly Tic Tac Toe looked like fun, so I downloaded the software myself and played a game. Here’s a screenshot of me having beat the computer on the Klein Bottle:

Screenshot posted with permission

Because it’s a Klein bottle, when you move down to the bottom it’s the same as moving up, but with left and right switched; the sides are likewise connected, although you stay in the same row. You can even hold down the cursor and move the board around to see how it behaves like an infinite board. It reminded me a little bit of Möbius Chess.

There’s a bunch of other free stuff, too, at Jeff’s main site of Topology and Geometry Software, like Kali for making wallpaper pattern designs and the 3d Kaleido Tile. (I had a lot of fun moving the center point and seeing solids morph into other solids.)

Meanwhile, the students had moved on to exploring the shape of the universe. Not too bad for a Monday morning.

Friday Software Review: Texify

Have you ever wanted to include mathematics on your website (or in a blog post, or in a forum, or…)? If you know how to use LaTeX, you can do just that, and make it look purty, too.

Friday Software Review: GAP

After a two-week hiatus, we’re back with another installment of FSR. This week we look at GAP (Groups, Algorithms, Programming), a “system for computational discrete algebra, with particular emphasis on Computational Group Theory”. GAP is another freebie, and it has a very large user community that has produced dozens of add-on packages to increase its functionality.

Friday Software Review: Maxima

This week we’ll look at Maxima, a computer algebra software (CAS) program. From the website:

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors…Maxima can plot functions and data in two and three dimensions.

It has many of the same functions and capabilities as Maple and Mathematica and costs several hundred dollars less.

Friday Software Review: GeoGebra

In the first of what I hope to be a (nearly) weekly column, I’ll review GeoGebra, a free geometry software package.

GeoGebra is similar to Geometer’s Sketchpad in that you can perform all of the standard ruler-and-compass constructions (e.g., bisecting a segment, bisecting an angle), but you can also enter algebraic equations. So if you want to work with a circle, you can enter the equation directly, or you can create a point and use it as the center to draw a circle with the “circle” tool (GeoGebra will then find the equation for you, if you want). Here’s the construction of a regular pentagon in progress (click for full-size):

The interface is fairly intuitive. I didn’t need to refer to the documentation at all to do my first construction (the pentagon). In my attempt to construct the heptadecagon, round-off error caused the last side to be off slightly, and I haven’t tried again lately (because really, who wants to follow the instructions to construct a 17-sided polygon twice?), so I don’t know if that has been fixed.

GeoGebra is Java-based, so it’s a little slow to load (as are all Java apps), but you can download the whole thing and install it locally. It’s a nice thing to have when you’re not at school and can’t get to Geometer’s Sketchpad, and it generates very nice pictures if you need to include some in a document (LaTeX, Word, a blog).

As a big fan of free software (which will become more apparent the more I review), I like GeoGebra. If you ever need a little help with those geometry constructions, you can’t find a cheaper solution.