Transformers

Here is a guided exploration of geometric transformations using GeoGebra. There is a brief introduction to the software, followed by some sample exercises.  The most important thing is to explore (I did call it an exploration). Play around with the program and see what you can do.  If you're up for it, there are two additional challenges, as well as a few interesting applications to evolutionary biology and computer animation.  Enjoy.

The (Sinusoidal) Sound of Music

Ever wonder how they can get keyboards and electric pianos to sound so much like the real deal?  The answer, of course, is through mathematical modeling (but you knew that, right?).  Specifically, engineers use combinations of trigonometric functions to model complex sound waves so that your keyboard's circuitry can mimic all those vibrating strings.  If that's not enough motivation to watch the video, you get to see me play the piano a little, which should be good for a laugh.  The sound quality--which, really, is the whole point of this exercise--is not super after recording, formatting, and uploading to YouTube, but hey, you still get to laugh at me.  Enjoy the performance.

The song, by the way, is "My Immortal" by Evanescence.  There was much speculation.

Circular Logic

Here is an extremely brief introduction to conic sections.  Like, incredibly brief. Basically it just explains, via an extremely slick video, why they're called conic sections.  The rest of the video is about circles, which make up one small, specific category of conic sections.  Still interested after this?  You'll love Pre-Calc.

Powerball Payoffs

So you did it.  Against all advice from your math teachers, you played the lottery. And you won.  Now how are you going to get paid?