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Thread: Hyperbolic Line Segment Tool - Venema

  1. #1

    Hyperbolic Line Segment Tool - Venema

    Does anyone know a good method that I can use to build a Poincare line segment in The Geometer's Sketchpad? I can build a ray and a line tool no problem but my ray's either disappear or "loop around". Problem 14.2.3 gives you two hints for building a ray tool and I used the second method to build a "reliable" ray by finding inversion points for B and creating an arc through three points. Then finding the intersection of the Poincare disk and the arc, hiding the first line I created and then creating another arc through A, B and the intersection point on the circle.

    I tried using that same method to create a line segment tool, but the line segment falls apart if I try and move any of the points around. I can move the ray around and it is very reliable.

  2. #2

    Sketchpad actually comes with a fairly extensive set of Poincare tools. You'll find them by choosing Help | Sample Sketches and Tools | Advanced Topics | Poincare Disk Model of Hyperbolic Geometry. The nine custom tools in that collection include a line tool and a segment tool. (They don't include a ray tool, however, so you've at least in part extended the available tools.)

    It's terrific that you're building your own tools, of course, so you'll most likely just want to inspect the segment tool using the Script View and Object Properties to see how it was done in a reliable way.

    Post again, please, if you have any difficulty figuring out how to make your own version of the tool work.


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