The Klein Disk

Below is an applet with drawing tools for the Klein Disk model of elliptic geometry.
(Be patient; the applet takes a few seconds to load.)
Use the "disk" menu (tool menu furthest to the right) to access the tools of hyperbolic geometry in this model.

Bugs and Features:

• This applet uses stereographic projection to represent elliptic geometry, and can therefore be used to model either double elliptic geometry (spherical geometry) or single elliptic geometry (the Klein Disk).
• To work in spherical geometry, interpret the interior of the disk as the northern hemisphere, and the exterior of the disk as the southern hemisphere.
• To work in the Klein Disk, ignore the points in the exterior (except possibly as part of constructions).
• Elliptic distances are given assuming spherical geometry. (The sphere is assumed to have unit radius.)
  To determine distance in the Klein Disk, distances d greater than π/2 should be replaced by π/2−d.
• The compass tool has the inputs in the wrong order...
  Select the center first, then the other two points.
• The elliptic line tools do not work if one point is on the unit circle.
  (Possible workaround: Construct Euclidean circles through three points, including the antipodal point.)
• The elliptic line tools do not work for (parts of) diameters. Use Euclidean tools instead.
  (Possible workaround: Construct the line between points not along a diameter, then move them.)
• The elliptic angle tool does not work if one side is (part of) a diameter. Use Euclidean tools for angles at the origin.
  (Possible workaround: construct the angle away from the origin, then move it.)

Acknowledgment: The underlying applet Klein2.ggb was written by Tevian Dray in 2016 and revised in 2022. It may be used under a by-nc-nd Creative Commons license.