Phrase guide

point at infinity

noun · 3 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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Pronunciation

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1

noun

Meaning 1

An asymptotic point in 3-dimensional space, viewed from some point, at which parallel lines appear to meet and which in perspective drawing is represented as a vanishing point.

Definition source: English Wiktionary via Wiktextract

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

Any point added to a space to achieve projective completion.

Definition source: English Wiktionary via Wiktextract

Qualifier: Euclidean projective geometry

Topics: geometry, mathematics, sciences

Examples

  • 1960, Roger A. Johnson, Advanced Euclidean Geometry, Republished 2007, page 45, In the geometry of inversion, therefore, it is usual to sacrifice the line of points at infinity which is so useful in other fields, and adopt the convention of a single point at infinity, the inverse of the center of the circle of inversion.
  • 1997, Susan Addington, Stuart Levy, Lost in the Fun House: An Application of Dynamic Projective Geometry, James King, Doris Schattschneider, Geometry Turned On: Dynamic Software in Learning, Teaching, and Research, page 159, To unify the treatment of concurrent and parallel lines, define a point at infinity for each family of parallel lines, and declare each point at infinity to lie on each of the parallel lines that define it. [...] Now parallel lines meet at infinity, and vanishing points are the images of points at infinity.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

An ideal point.

Definition source: English Wiktionary via Wiktextract

Usage: excessive

Topics: geometry, mathematics, sciences

Examples

  • 2007, Maurice Margenstern, Cellular Automata in Hyperbolic Spaces, Volume 1: Theory, page 66, As we have seen, points at infinity behave as ordinary points: a single line passes through two distinct points at infinity or through a point in the plane and a point at infinity. This representation of the points at infinity is a difference between the disc and the half-plane models of Poincaré, [...] .

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.