Circumscribing a Hyperbolic Triangle
This page requires a java-enabled browser for correct functioning. You can drag the points labelled A, B, and C around with the mouse, and the other points will move accordingly.
|In hyperbolic geometry, not all triangles can be circumscribed by a circle. If there were a circumscribing circle, its center O must lie on the common intersection of the perpendicular bisectors of the three sides. In the figure above, if you move B and C further apart, you can see how this intersection moves off the edge of the hyperbolic disk. While the software still draws (part of) the circle, notice that it describes its radius as a complex number; this is an artifact of the way that the program represents the circle which is no longer "really there".|
Java image created using Cinderella by Scott Sutherland on March 29, 2004 .