Sources
open directory project
Help build the largest human-edited directory on the web.
Submit a site - Become an editor
Wikipedia. Licensed under the GNU Free Documentation License.
Are you an expert in this subject? Join the discussion and share your knowledge at Wikipedia.org.
Circular points at infinity
From Wikipedia, the free encyclopedia
In projective geometry, the circular points at infinity in the complex projective plane (also called cyclic points or isotropic points) are
- (1: i: 0) and (1: −i: 0).
Here the coordinates are homogeneous coordinates (x: y: z); so that the line at infinity is defined by z = 0. These points are called circular points at infinity because they lie at infinity, on that line, and they also lie on all circles. In other words, both points satisfy the homogeneous equations of the type
- Ax2 + Ay2 + 2B1xz + 2B2yz − Cz2 = 0.
The case where the coefficients are all real gives the equation of a general circle (of the real projective plane).
The circular points at infinity are the points at infinity of the isotropic lines.
The cyclic points are invariant under translation and rotation.