For teaching parametric curves, I've been thinking about a system that would let students move their mouse around on the screen, and would plot the corresponding x and y values as functions of time. I don't know what existing software would let me do this, so I wrote my own little page for it. It gave me a fun opportunity to play with the canvas HTML element, some light javascript, and more. I learned how to cycle through colors!

Anyway, if you'd like to play with it, it is here. I've found that it only works in Firefox 3.5, and Google Chrome. Perhaps you'll have other luck with other browsers.

To use the page, first move your mouse to the very bottom right corner of your browser window (or possibly your whole screen, it might depend on your setup), and then click the 'Start' button (like the directions on the page say). As you move your mouse around, the upper-left graph should match your motions. The upper-right graph shows the y-coordinate as a function of time, and the lower-left graph shows the x-coordinate as a function of time. I always think that when separating the functions this way, interpreting the graph for x(t) is somewhat tricky, because x values are vertical, where we generally think of them as horizontal things. So the 'Flip x/t' button will swap coordinates in that x(t) graph. Now horizontal coordinates in the lower-left graph for x(t) correspond directly to horizontal coordinates in the upper-left graph for (x(t),y(t)).