## 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 ... [* garrett@math.umn.edu
*]
The University of
Minnesota explicitly requires that I state that *"The views and
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