21. This topological space, the complex plane plus the point at infinity , is known as the extended complex plane. 22. Idealized directions are referred to as points at infinity , while idealized horizons are referred to as lines at infinity. 23. For the parabola, the center of the directrix moves to the point at infinity ( see projective geometry ). 24. The equation should be studied on the Riemann sphere to include the point at infinity as a possible singular point. 25. The stabilizer of any point ( a " point at infinity " ) is the affine group of a line. 26. For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is a conformal map. 27. The projective harmonic conjugate of such a " midpoint " with respect to the two endpoints is the point at infinity . 28. The modular group acts continuously on this compactification, but they showed that their compactification has strictly more points at infinity . 29. For real hyperelliptic curves, there are two points at infinity , \ infty _ 1 and \ infty _ 2. 30. He introduced the method of the critical points at infinity , which is a fundamental step in the calculus of variations.
