Dynamic Geometry workshop: 2

Sketchpad Continued — 3rd session Sebastian Lisken
lisken@Mathematik.Uni-Bielefeld.DE

Further remarks on constructions and measurements

One important construction which we will use today is the locus. You need a locus in a situation when you see a dependent point move in an interesting way as another point is dragged along some path.

Naturally you will want to want to turn that dependent point into some kind of pencil. You can do exactly that by turning on the trace property for that point (in the "Display" menu). But a pencil is not a very "dynamic" device: you have to do the drawing (dragging) yourself, and you must repeat the drawing process after moving some "parameters".

A locus is a more "intelligent" kind of pencil. It is the set of all locations of that dependent point as the other (the driver point) is moved along the path. It is recalculated every time you drag objects around. To construct a locus, simply select the driver point and the "driven" point and use the "Construct Locus" menu item.

One important feature of measurements is that you can "put back" their values into new elements of the script. You can even make calculations to get some new numbers from measured values and put these back. Without this feature, it would be impossible to produce the gear mechanism that was included in last week's cog-wheel construction.

We will now take a short look at some features that make Sketchpad a general-purpose mathematical presentation tool rather than "just" a geometry program.

Coordinates (and Calculations and Graphs)

Axes are a convenient mechanism to do all kinds of analytic geometry. Anything that you can measure (or calculate with Sketchpad's calculator) can be transported into the coordinate system of a sketch.

Here is a tutorial on how to create a standard function graph. Open the sketch (by a single click on the image on the left). In the sketch, double-click the button named "Part 1" (two fast clicks.)

You don't actually need Sketchpad's coordinate system for analytic geometry. Remember that we did measure x values before — how could we do the reverse and put a calculated value onto a line? With "skewed" coordinate axes, a journey into 3D-space graphs seems possible. If we change the mathematics of measuring, even a perspective view can be done.

Buttons

You have seen quite a lot of what buttons can do. They can

hide and show objects,
move points to where other (possibly hidden) points are,
start an animation,
and also start a whole sequence of actions (i.e. other buttons).

Buttons are easy to construct, just like any other dependent object. You select the relevant objects and use the items in the "Edit | Action Button" submenu. (Unfortunately that's quite far away from the "Construct" menu, where the other constructions are.)

For a pair of Hide/Show buttons, select whatever you want to show and/or hide.
For a Movement button, select an even number of points in the correct order: Point 1 will be moved to Point 2, Point 3 to Point 4, ...
For an Animation button, select a point and a path, possibly another point and another path, and so on. The points can be either free or restricted to the paths that you want to use. You must get to know the "animation menu" which appears when select "Edit | Action Button | Animation..."
For a Sequence button, select the buttons you want the sequence to use, in the correct order (!). Any kind of button can be used. You can cause a delay in the sequence by giving some buttons an "In-Sequence delay". Select the Information tool (the question mark) and double-click one of your buttons. You can specify a number of seconds. Sketchpad will pause for that time after the button is executed as part of a sequence.

Try to "spice up" one of your previous sketches with buttons. If you have no suitable sketch at hand, try these two: A standard cardioid construction from last week, or a far-too-full triangle sketch that shows interesting things, but really needs structure and perhaps explanation.

One final hint: You can select one button before saving your sketch. That will create an automatic button which will be executed when you open your sketch. With carefully prepared sequence buttons, you can almost become your own film director ...

Thanks, and goodbye

You can investigate these links if you want to use Sketchpad further after the course.

Sketchpad homepage from the producers, Key Curriculum Press. Includes an Online section with numerous links to Sketchpad activities on the web.
My introduction to JavaSketchpad, an applet that displays sketches on Web pages.

Nov 7, 1999