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:
“Loving a baby is a circular business, a kind of feedback loop. The more you give the more you get and the more you get the more you feel like giving.”
—Penelope Leach (20th century)
“Only that which points the human spirit beyond its own limitations into what is universally human gives the individual strength superior to his own. Only in suprahuman demands which can hardly be fulfilled do human beings and peoples feel their true and sacred measure.”
—Stefan Zweig (18811942)