Hyperbolic Plane

In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can intersect, or can be hyperparallel (diverge from each other in both directions).

Taimina (2006) has crocheted numerous hyperbolic planes, originally as an instructive device.

See also

Apeirogon, Euclidean Plane, Hyperbolic Tiling, Klein Quartic, Poincaré Hyperbolic Disk, Riemann Sphere, Rigid Motion

Explore with Wolfram|Alpha

References

Anderson, J. W. "A Model for the Hyperbolic Plane." §1.1 in Hyperbolic Geometry. New York: Springer-Verlag, pp. 1-7, 1999.Update a linkTaimina, D. "Mysteries of the Hyperbolic Plane." Carleton College News, May 18, 2006. http://apps.carleton.edu/news/?content=content&module=&id=193307

Referenced on Wolfram|Alpha

Hyperbolic Plane

Cite this as:

Weisstein, Eric W. "Hyperbolic Plane." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicPlane.html

Subject classifications