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:
“Oh Lolita, you are my girl, as Vee was Poe’s and Bea Dante’s, and what little girl would not like to whirl in a circular skirt and scanties?”
—Vladimir Nabokov (1899–1977)
“He is the best sailor who can steer within the fewest points of the wind, and extract a motive power out of the greatest obstacles. Most begin to veer and tack as soon as the wind changes from aft, and as within the tropics it does not blow from all points of the compass, there are some harbors which they can never reach.”
—Henry David Thoreau (1817–1862)