The point at infinity, also called ideal point, of the real number line is a point which, when added to the number line yields a closed curve called the real projective line, . The real projective line is not equivalent to the extended real number line, which has two different points at infinity.
The point at infinity can also be added to the complex plane, thereby turning it into a closed surface (i.e., complex algebraic curve) known as the complex projective line, also called the Riemann sphere.
The concept of infinity point admits several generalizations for various multi-dimensional constructions.
Read more about Point At Infinity: Projective Geometry, Hyperbolic Geometry, Other Generalisations
Famous quotes containing the words point and/or infinity:
“There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”
—A.J. (Alfred Jules)
“As we begin to comprehend that the earth itself is a kind of manned spaceship hurtling through the infinity of space—it will seem increasingly absurd that we have not better organized the life of the human family.”
—Hubert H. Humphrey (1911–1978)