Non-Euclidean Geometry

This applet allows click-and-drag drawing in the Poincare model of the (hyperbolic) non-Euclidean plane, and also motion. The circular arcs drawn by mouse drags are the geodesics (straight lines) in this model of geometry.

In "move" mode, click-and-drag slides the whole picture in the direction of the mouse drag. This is analogous to ordinary "sliding" of objects in Euclidean space; however, in this non-Euclidean geometry the Euclidean picture of it makes things appear to become smaller as they move toward the edge. But, in fact, in terms of the non-Euclidean geometry, despite appearances, these motions preserve distances and angles. The preservation of angles should be detectable if one keeps in mind that the angles are angles between the arcs of circles at their point of intersection.

Since the bounding circle is "infinitely far away", the motion of the picture does not exactly parallel the mouse drag motion, but instead moves about the same non-Euclidean distance as the Euclidean distance moved by the mouse. So the picture will appear to lag behind the mouse.

© 1997-1998, Paul Garrett ... [ ]
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