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)
“New York, you are an Egypt! But an Egypt turned inside out. For she erected pyramids of slavery to death, and you erect pyramids of democracy with the vertical organ-pipes of your skyscrapers all meeting at the point of infinity of liberty!”
—Salvador Dali (1904–1989)