Saturday, October 10, 2009
My favorite free math stuff
Although I have licensed copies of Mathematica, Mathcad, and Maple, my favorite grapher is Winplot. Plots are easy to create and highly customizable. Winplot handles parametric, polar, and implicit 2D graphs and wireframe 3D plots, with numerous other nifty features.
Winplot is one of several clever programs written by Rick Parris of Phillips Exeter Academy. You can download his free programs from http://math.exeter.edu/rparris/.
Another under-utilized program is Markus Hohenwarter's GeoGebra. If you ever wanted to use (or are using) Geometer's Sketchpad or Cabri, you might want to give this one a try. Like GS or Cabri, GeoGebra allows you to make a geometric construction based on points and/or lines of your choice, then shows you how the constructed object changes as you use the mouse to alter the defining points or lines.
But unlike GS or Cabri, GeoGebra also has an algebra window that records the algebraic representation of the geometric objects. You can either modify an algebraic definition and watch in real-time the change in the figure, or alter the figure and see how parameters change in the algebraic description.
Read more about GeoGebra in articles in the online journal Loci (http://tinyurl.com/yk8w3ks and http://tinyurl.com/yz2yjkj), or download the free program directly from http://www.geogebra.org/cms/ .
Barbara Kaskosz and Doug Ensley's Flash Forum has lots of clever applets for free download or use online. I particularly like the "Visualizing Regions for Double Integrals" (http://tinyurl.com/ygcfulh) by Barbara and Lewis Pakula. You enter the limits of a double integral (in rectangular or polar coordinates) and the appropriate region is sketched. Or you can ask for a practice problem, and you are given a region for which you need to determine the coordinate system and corresponding limits to define it.
The Flash Forum also has a 3D function plotter, and graphers for surfaces defined parametrically in rectangular, cylindrical, or spherical coordinates (http://tinyurl.com/yhx45lx).
But my favorite applet is "Terminate the Terminator!", (http://tinyurl.com/yzn9m25) a game to introduce radian measure and polar coordinates. It was originally created by my colleague Bob Martinez in Mathcad, but the online version is in Flash.