The Poincaré Disk

This directory contains a base sketch and tools for interactive investigation of hyperbolic geometry using the Poincaré disk model. For example, one can easily discover that the construction of the incircle of a triangle that works in the Euclidean plane also works in the hyperbolic plane.

These documents are scripts as opposed to sketches: be sure to try them as scripts tools by setting the script tool directory to the directory in which you store them. The center and radius of the disk are marked as automatic givens in the scripts so that it is only necessary to choose the givens relevant to the specific construction when you use these scripts as script tools.

The original versions of the scripts were created by Mike Alexander when he at the University of Washington. The versions here have been modified to use arcs.

The scripts on this page are available individually (below) or can be downloaded as a package.



Poincaré Disk Starter. Start with this sketch, containing a circle properly labelled for use with the script tools.
Angle Bisector. Given three points, bisects the angle defined using the second point as the vertex.
Circle By Center+Point. Given two points, constructs the circle whose center is the first point and which passes through the second point.
Circle By Center+Radius. Given two points, constructs the circle whose center is the first point and which passes through the second point.
Line. Construct a hyperbolic line from two points.
Measure Angle. Given three points, measure the hypberbolic angle defined with the second point as the vertex.
Measure Distance. Measure the hyperbolic distance between two given points.
Perpendicular Bisector. Given two points, construct the perpendicular bisector of the segment joining them.
Perpendicular thru Pt off Line. Given three points, use the first two to define a line and the third to determine a perpendicular to the line passing through the point.
Perpendicular thru Pt on Line. Given two points, construct a perpendicular to the line defined by the two points through the first point.
Segment. Construct a hyperbolic segment determined by the two given points.

Return to the Foyer.

Sketches, scripts, and web pages by Bill Finzer and Nick Jackiw.