In this section, we give detailed information on how to obtain and install the tools. This process essentially consists of the following steps:
Running a script manually: Every Geometer's Sketchpad script accepts certain geometric objects as inputs ("Givens") and returns a requested geometric object as an output. Running a script manually amounts to opening the appropriate script, informing Sketchpad of the "givens" for the script, then "playing" the script. For example, suppose one wants to draw a non-Euclidean circle having center O and radius OP in the Klein model. First open the appropriate template file (klnstrt.gsp in this case) as detailed in #4 above. Plot (and label) two points O and P, which will be the respective center and point on the circle. The script that performs the circle construction is titled klncntrpt.gss, and this file needs to be opened as well. This is done by selecting "Open" from the "File" menu option, then selecting "klncntrpt.gss" from the appropriately named directory, "klein" in this case (see #2 above). When these steps are completed, the Sketchpad desktop should look something like this:
|(The above figure comes from a Windows 98 version of Geometer's Sketchpad; the desktop may appear slightly different on different platforms.) In this picture, the script file appears on the upper right-hand of the desktop. Click on the image for an enlarged view.|
|A closeup of an open script file.|
To construct the desired non-Euclidean circle, the script requires four pieces of information: the two points which define the circle and the two points that define the Klein disk. As a result, the script kcntrpt.gss for a Klein circle accepts as "Givens" four different objects: the point defining the center of the Klein disk (called "K-Disk center"), and a point on the boundary of the disk (abusively called "K-Disk radius"), together with the center O of the circle and a point P on the circle. To construct the circle, highlight the givens in the appropriate order by holding down the "Shift" key while selecting the givens in your sketch in the correct order: click on the point "K-Disk center," then click on the point "K-Disk radius," then click on your center point O, and finally click on the point P which will lie on the desired circle. (Remember to hold down the "Shift" key while making these selections.) At this point, all of your givens should be highlighted. If the script becomes hidden on your desktop because of these actions, you can bring it on top again by selecting it under the "Work" menu option. Now play the script by clicking on the "Play" button on the tool:
Sketchpad should construct the desired circle, and you should be able to watch the program performing the steps in the construction. Click on the "Fast" button to have the construction finished more rapidly. The figure that should result is given in the picture below (click on the figure to see an enlarged view):
Running scripts automatically using a script tool directory. Running scripts manually can be cumbersome, particularly if one needs to use many different tools in a sketch: the desktop ends up being cluttered with open scripts. Automatic scripting provides a faster and cleaner way of using scripts. The idea is to create a new tool on the left-hand toolbar on the desktop by telling Sketchpad where one's scripts are stored. Then when one wants to use a particular tool, it can simply be selected from the toolbar and used as one would use the usual line-drawing or circle-drawing tools. For example, suppose as above, one wants to draw a non-Euclidean circle having center O and radius OP in the Klein model. To do this, one must first set the Geometer's Sketchpad "script tool" directory to "klein" (or to whichever directory the Klein disk tools have been stored). One way to set this directory is by editing user "Preferences." Select "Preferences" under the "Display" menu, then click "More," since setting the script directory is on the second page of options. Choose the "Set" option under the "Script Tools Directory:" and set the directory to the directory in which the appropriate tools are stored (directory "klein" in this example). Geometer's Sketchpad has additional documentation on this and on other ways to set your script tools directory. Once you have chosen a valid directory, a "script tools" icon,
will appear on the left side of your Sketchpad desktop, just below the Object Information ("?") tool.
Next, one needs to open the appropriate template file (klnstrt.gsp in this example), and to make sure that the disk center and "radius point" are labeled properly. In our particular example, the center must be labeled "K-Disk center" and the point on the boundary of the disk must be labeled "K-Disk radius." One can see from script definition for kcntrpt.gss (see the picture above) that the "Givens:" include "Auto-K-Disk center" and Auto-K-Disk radius." When using automatic scripting, Sketchpad looks for these "Auto" points by name, so if the Klein disk is not labeled in this way, the automatic scripting will fail.
If the script directory has been set up properly and a properly labeled template file has been opened, then automatic scripting is straightforward. One can select the appropriate hyperbolic tool by clicking on the script tool button, then scrolling down to the desired tool (in our example, this is the tool entitled "Klein Circle by center and point":
|Click on the image for an enlarged view.|
Once the script tool has been selected, the mouse pointer should appear with a small circle at its tip:
Now if one selects the other desired givens for the script by clicking in the sketch, Geometer's Sketchpad should perform the desired construction automatically. In our Klein-circle example, after selecting the proper script tool, if one clicks on two points in the interior of the Klein disk (corresponding to the two remaining givens, center O and point P on the circle), Geometer's Sketchpad will construct the desired hyperbolic circle. In fact, after clicking on the center point O, the circle will be generated dynamically; Sketchpad will construct the Klein-circle centered at O and passing through the current location of the pointer, and will continue to do so until the second click:
|Click on the image for an enlarged view.|