Installing and Using the Hyperbolic scripts in Geometer's Sketchpad version 3

I developed the tools described here using Geometer's Sketchpad version 3.   Key Curriculum Press released version 4 of Sketchpad in 2001.  This newer version of Sketchpad accesses and utilizes script tools in a substantially different way from version 3.  Therefore, I wanted to keep the version 3 tools available for those who do not have version 4 available.  On this page, you can find

• Hyperbolic tools for the Beltrami-Klein Disk.
• Links to hyperbolic tools for the Poincaré disk.
• Hyperbolic tools and links to other hyperbolic tools for the Poincaré half-plane.
• Instructions on installing and using the tools.

Note that all the tools and instructions below were written for users of Geometer's Sketchpad version 3.  Sketchpad version  4.0 users should click ----> here <----

Klein Model Tools

klein.zip

All the Klein model scripts in one ZIPPED package (Recommended)


The zip file contains all of the Klein disk model scripts listed below. If you don't have access to an unzipping utility, you could download one from Pkware. If you choose to download the scripts individually, please read the following warning about Netscape downloads.


klnstrt.gsp	Klein model template Geometer's Sketchpad file.
kline.gss	Script to construct a Klein line.
ksegmnt.gss	Script to construct a Klein segment.
klength.gss	Script to measure the Klein length of a line segment.
kangmea.gss	Script to measure an angle in the Klein model.
kangbis.gss	Script to bisect an angle in the Klein model.
kprpon.gss	Script to construct the Klein perpendicular through a given point on a given Klein line.
kprpoff.gss	Script to construct the Klein perpendicular through a given point not on a given Klein line.
kprpbis.gss	Script to construct the perpendicular bisector of a Klein segment.
kcntrpt.gss	Script to construct a Klein circle given its center and a point on the circle.
kcntrrd.gss	Script to construct a Klein circle given its center and two points which determine the radius.

In creating scripts for the ten "standard" hyperbolic constructions listed at the top of the page, it proved useful to create other tools which are particularly useful in the Klein model. One particular difficulty with the Beltrami-Klein model is that unlike the Poincaré models, Klein circles are not Euclidean circles - they are ellipses. As such, in Geometer's Sketchpad, they must be drawn as loci. This creates a practical problem: Sketchpad does not know how to intersect loci. Below, then are some additional tools which allow one to find the intersection of Klein circles with other Klein circles, Klein lines, and Klein segments. All these tools are available in the complete file klein.zip.

kpole.gss	Script to construct the pole of a Klein line.
kmidpt.gss	Script to construct the midpoint of a Klein segment.
kreflpt.gss	Script to construct the reflection of a given point about a Klein line.
kintcirc.gss	Script to find the intersection point(s) of two Klein circles.
kintlncr.gss	Script to find the intersection point(s) a Klein circle with a Klein line.
kintsgcr.gss	Script to find the intersection point(s) a Klein circle with a Klein line segment.
kd_to_pd.gss	Script to map a point in the Klein disk isomorphically to its corresponding point in the Poincaré disk.

Poincaré Disk Model Tools

• Mike Alexander (with modifications by Bill Finzer) has created scripts for the ten "standard" constructions for the Poincaré disk model. They provided inspiration for my scripts in the Klein disk and Poincaré half-plane model and can be found here.
  
• For the Beltrami-Klein model, I wrote a tool (kd_to_pd.gss) which maps points in the Klein disk isomorphically to their corresponding points in the Poincaré disk. The natural isomorphism is described in Greenberg's text Euclidean and Non-Euclidean Geometries , 3rd edition (Freeman Publishers), p. 236. I have written a corresponding tool which inverts the process (pd_to_kd.gss) which maps points in the Poincaré disk isomorpically to their corresponding points in the Klein disk.

Poincaré Half-Plane Model Tools

• Dan Bennett has created scripts for the first four constructions listed at the top of this page (constructing lines and segments, and measuring length and angles) in the Poincaré half-plane model. His tools can be found here.
• Tim Peil has also written several scripts for the Poincaré half-plane. His tools can be found here.
• The tools I have written for the Poincaré half-plane complete the remaining constructions for the "standard" ten constructions given at the top of this page. Though some of my tools appear to reproduce the work of others, the constructions do not rely on coordinate (analytic) geometry. See the descriptive file scripts.pdf for more information:
  

poinhalf.zip

All my Poincaré half-plane model scripts in one ZIPPED package (Recommended)

The zip file contains all of the Poincaré half-plane model scripts listed below. If you don't have access to an unzipping utility, you could download one from Pkware. If you choose to download the scripts individually, please read the following warning about Netscape downloads.-

poinhalf.gsp	Poincaré half-plane model template Geometer's Sketchpad file.
phlength.gss	Script to measure the Poincaré half-plane length of a line segment.
phangbis.gss	Script to bisect an angle in the Poincaré half-plane model.
phprpon.gss	Script to construct the perpendicular through a given point on a given line in the Poincaré half-plane model.
phprpoff.gss	Script to construct the perpendicular through a given point not on a given line in the Poincaré half-plane model.
phprpbis.gss	Script to construct the perpendicular bisector of a Poincaré half-plane segment.
phcntrpt.gss	Script to construct a Poincaré half-plane circle given its center and a point on the circle.
phcntrrd.gss	Script to construct a Poincaré half-plane circle given its center and two points which determine the radius.

In creating scripts for the ten "standard" hyperbolic constructions listed at the top of the page, it proved useful to create other tools which are particularly useful in the Poincaré half-plane model. Below are additional tools which allow one to find midpoints and construct reflections in the half-plane. These tools are available in the complete file poinhalf.zip.

phmidpt.gss	Script to construct the midpoint of a line segment in the Poincaré half-plane model.
phreflpt.gss	Script to construct the reflection of a given point about a line in the Poincaré half-plane model.

Installing the Tools

What follows are the instructions for installing and using the hyperbolic tools in Geometer's Sketchpad version 3.  Users of version 4 should click here for those instructions.  If you find the instructions that follow are inadequate, you might want to look at the article "The Hyperbolic Toolbox" that I wrote for the Journal of Online Mathematics and its Applications.  More complete instructions are provided there.

0.	Make sure that you have a working copy of Geometer's Sketchpad version 3. The software can be purchased from Key Curriculum Press. You can download a free demonstration version of Geometer's Sketchpad from the Key Press site. The demo version is similar to the full version, but you cannot save, print, or export your work.  As of February 2003, I am unsure how available version 3 of Sketchpad is ...
1.	Download the desired tools into a directory. I recommend creating separate directories called "klein", "poincare", and "poinhalf", where you can store the scripts corresponding to the three different models. You can download my Klein model package , my Poincaré half-plane model package , and you can get other Poincaré tools from Alexander and Finzer, Bennett, and Peil. See my hyperbolic tools page for more information on these tools.
2.	Unzip any zipped files. If you downloaded "klein.zip," "poincare.zip," or "poinhalf.zip", unzip the files in the directory in which you will be storing the tools. You can get an unzipping program from Pkware.
3.	Set your Geometer's Sketchpad script tools directory to the appropriate directory for your constructions (e.g. "klein", "poincare", etc). See the Sketchpad documentation.
4.	Load the appropriate Sketchpad template file to begin. If you're using the Klein tools, use the startup file "klnstrt.gsp" which has an appropriately labelled Klein disk. If everything has been downloaded and set up properly, the construction tools should be available from the Sketchpad script tool. The templates for the Poincaré disk and Poincaré half-plane models are "poinstrt.gsp" and "poinhalf.gsp", respectively.

Problems? Drop me an email at szydliks@uwosh.edu.

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If you have any questions or find any errors on this page or in my tools, please notify me at szydliks@uwosh.edu. Thanks!