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:
“Consider a man riding a bicycle. Whoever he is, we can say three things about him. We know he got on the bicycle and started to move. We know that at some point he will stop and get off. Most important of all, we know that if at any point between the beginning and the end of his journey he stops moving and does not get off the bicycle he will fall off it. That is a metaphor for the journey through life of any living thing, and I think of any society of living things.”
—William Golding (b. 1911)
“We must not suppose that, because a man is a rational animal, he will, therefore, always act rationally; or, because he has such or such a predominant passion, that he will act invariably and consequentially in pursuit of it. No, we are complicated machines; and though we have one main spring that gives motion to the whole, we have an infinity of little wheels, which, in their turns, retard, precipitate, and sometime stop that motion.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)