point at infinity
A 'point at infinity' is a theoretical concept used to simplify and extend geometric and mathematical analyses.
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Definition
C1Projective Geometry
(technical, academic)An idealized location where parallel lines appear to meet, extending the Euclidean plane.
Example
- In projective geometry, a point at infinity helps in visualizing parallel lines as converging.
C2Euclidean Projective Geometry
(technical, academic)A theoretical point added to a space to complete it projectively.
Example
- Adding points at infinity allows for a more comprehensive treatment of geometric transformations.
C2Hyperbolic Geometry
(technical, academic)An idealized point representing the boundary of hyperbolic space.
Example
- In hyperbolic geometry, points at infinity help define the limits of the space.
C2Complex Analysis
(technical, academic)A conceptual point added to the complex plane to manage functions approaching infinite values.
Example
- The point at infinity in complex analysis aids in understanding the behavior of complex functions.
Similar
Terms that have similar or relatively close meanings to "point at infinity":