# GeoGebra

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## Hyperbolic Geometry in the Poincaré Disk

Here you will find a complete environment for exploring and investigating concepts and ideas in hyperbolic geometry using the Poincaré Disk. There are sixteen tools present in order to provide a dynamic hyperbolic environment.
9

Material Type
Worksheet
Tags
hyperbolic  geometry  environment  poincaré  poincare
Target group (age)
19+
Language
English (US)

GeoGebra version
4.0
Views
7549
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## Write a comment

• hi
do u have some kind of construction manual?
sef
• — Shared by
• Do you mean instructions on how the tools were made or do you mean instructions on how to use the tools or do you mean something else?
• Hi
I mean how the tools were made
sef
• — Shared by
• I do have the files saved for the constructions of the tools. Going through the construction protocols in these files does a pretty good job of explaining how these were made. Some of the tools, like lines and and circles, require a bit more knowledge to follow. And I have documented these in a paper I am currently writing. If you like, I can consider posting this here or in the forum. Send me a PM. By the way, I have started a topic in the forum for this file here:

http://www.geogebra.org/forum/viewtopic.php?f=2&t=26927
• By the way, the angle tool was flawed and I uploaded a new file here with a correct tool for finding angles a couple of hours ago.
Regards,

• To make it even better ...
well nice Icon on the tools would be great, an it will help a lot.

But more important would it be, to customize the tool bar a bit. I would delete the tools that are not needed. Only movin and may be deleting is important. So, that name of you the choosen tool can be shown beside the tools. Now it is not shown, as there is not enough place. And the menu ... is it needed, too?
• Hi, thanks for this great tools!!!
I have some problem with the "Hyperbolic drop Perpendicular" tool.
If I drop a perpendicular from point P to line AB and call H the intersection point then, moving P, point H disappears everytime line PH crosses the center of the Poincaré disk.

By the way, some other very useful tools would be the reflections of a point in another point and in a line.

Thanks again!
Ciao
• — Shared by
• I'm afraid that is the nature of Geogebra. The hyperbolic lines are actually Euclidean circular arcs and that is exactly how Geogebra treats them. With the intersection of any two arcs, there are two possible points of intersection and Geogebra indexes these. I have not figured out exactly how it chooses one or the other but it's not hard to deal with. When H dissaspears, find the point of intersection again, let's say it's point I. Then type in

If[IsDefined[H],H,I]

This will create a new point, say K, that will always be at the intersection. Then you can hide points H and I.

Hope this helps.