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© Copyright 2003, Jim Loy
Cinderella's wicked step-sisters may have asked the same question (make her mop the floor over and over again, is my suggestion). But here, I will be writing about the program Cinderella.
I get email asking if Cinderella will draw histograms from the user's spreadsheet, or things like that. The answer is no. Well, it is possible, in a way, but there must be other software for that (Microsoft Works might do it, but don't use my imitation: Nothing Works). Then what does Cinderella do? Well, it is for geometry, and little else. It does what you can do with drawing tools (compasses and straightedge), with some enhancements (like animation, curve drawing, and non-Euclidean geometries). And there are many simple geometric drawings that you cannot do with Cinderella (because you are limited to compasses and straightedge tools). For example, you cannot trisect an angle; you cannot draw a sine wave, a spiral, or a cycloid, because you cannot draw a line segment equal to an arc. But with these severe limitations, you can sometimes get very impressive results. For some animations, Cinderella is the easiest tool that there is, but for most animations, Cinderella just cannot do it.
To get some idea of Cinderella's limitations, let's draw a moving automobile, with turning wheels. How do we go about that? Hm, I don't know. We need both uniform horizontal movement, and uniform circular movement, simultaneously. But, that means changing the lengths of an arc and a line segment at a constant rate at the same time. But, because of the compasses and straightedge limitations, that is impossible with Cinderella. Maybe it can be approximated in some way, but it won't be easy. This should be extremely easy with other animation tools, but it is essentially impossible with Cinderella. See the problem?
Let's do the above automobile animation from a different angle (a geometry saying). Let's capture still frames using the screen capture feature of my paint program, and create a GIF animation using my GIF animation program. Now this is quite easy using Cinderella, as long as I calculate how far to move the car and how far to rotate the tires myself. Almost any single frame can be drawn with Cinderella. Except that we can't smooth the lines, draw part of a curve, color the area between curves, draw dashed lines, have two points with the same label, etc. You see, Cinderella's visual effects are very limited, too. You'll have to use a more sophisticated paint program to fix up your images. I do that often.
OK, let's draw the graph of an equation. I already mentioned that we can't draw a sine wave. We also can't graph logarithms. We can draw conic sections and cubic equations (or higher powers), if we can figure out how to find the points with compasses and straightedge. Sometimes this is a big time bother. At other times it is easy and educational. Graph the set of points equidistant from a line and a circle (a parabola), not very difficult, and I didn't even have to deduce an equation. I like that.
If I choose two points exactly one unit apart, and then construct a third point one unit from each of them, I have defined the vertices of an equilateral triangle. With a paint program, I can draw these points with some accuracy, and my screen and printer may draw them with somewhat less accuracy. With Cinderella, I have defined these points with perfect accuracy (and my screen and printer show these with far from perfect accuracy). Cinderella has allowed me to define a length of exactly one, the integer one, not a real approximation. And the intersection that defines the third vertex is exactly one unit from the other two points. It is exactly sqrt(3)/2 from the midpoint of the opposite side of the equilateral triangle, not some decimal estimation of that. And so, many things that you can draw with Cinderella do not suffer when you blow up the picture to dozens of times larger.
So, Cinderella works well for some things, and does not work well for others. When it works (it may take some thought and creativity to figure it out), the results can be very impressive.
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