I stumbled upon an amazing find a few minutes ago: an OS X application called Graph Sketcher. It is developed and maintained by MIT, and very simply, Graph Sketcher lets you hand-draw graphs on a set of coordinate axes and then manipulate them by changing color and thickness, shading in areas underneath, and so on. You can add text annotations to the graphs and (apparently, haven’t tried this yet) graph spreadsheet data and add best-fit lines.
Why this software blows my mind should be clear to anybody who’s ever had to make up a handout, test, or lab for calculus or precalculus. In doing those course preps, you are constantly needing to make up graphs that have a certain look — inflection points in a specified place, strange asymptotic behavior, jump discontinuities, even just basic piecewise functions. You know how the graph ought to look, but to get the graph, you had to come up with a formula for it, plot it in a computer algebra system, and then export the plot as PDF or a graphics file and then import it into your document. This process is alternately impossible or maddeningly time-consuming. Or you could try to freehand it in a paint program, but those programs aren’t meant for precision, and while you might be able to get the behavior right, the result looks like crap.
But this software lets you just draw the lines where you want them, and then bend them using simple Bezier curve handles. Or you can tell it to plot certain points and connect the dots. Here’s a plot I just drew for a quiz:
I just drew four connected line segments for the curve and then bent them around until I got what I wanted. Voila — instant logistic function with a y-intercept at 2 and carrying capacity at 10. I didn’t have to diddle around with until I was blue in the face. (Even had I been inclined to do so, Maple still doesn’t work under Leopard so it’s moot.) Then one-click export to PDF, and I’m done. How many weeks might have been added back into my life that were otherwise wasted trying to get graphs to turn out right using formulas?
Best of all — it’s shareware. Who says there’s no good software out there for Macs?