Circular Points
The homogeneous form for the equation of a circle is x2 + y2 + 2axz + 2byz + cz2. The intersection of this curve with the line at infinity can be found by setting z = 0. This produces the equation x2 + y2 = 0 which has two solutions in the complex projective plane, (1, i, 0) and (1, −i, 0). These points are called the circular points at infinity and can be regarded as the common points of intersection of all circles. This can be generalized to curves of higher order as circular algebraic curves. A commonly known type of homogeneous coordinates are trilinear coordinates.
Read more about this topic: Homogeneous Coordinates
Famous quotes containing the words circular and/or points:
“The night in prison was novel and interesting enough.... I found that even here there was a history and a gossip which never circulated beyond the walls of the jail. Probably this is the only house in the town where verses are composed, which are afterward printed in a circular form, but not published. I was shown quite a long list of verses which were composed by some young men who had been detected in an attempt to escape, who avenged themselves by singing them.”
—Henry David Thoreau (1817–1862)
“Sometimes apparent resemblances of character will bring two men together and for a certain time unite them. But their mistake gradually becomes evident, and they are astonished to find themselves not only far apart, but even repelled, in some sort, at all their points of contact.”
—Sébastien-Roch Nicolas De Chamfort (1741–1794)