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Revision as of 18:17, 17 March 2025
Line (geometry)
A line in geometry is a straight one-dimensional figure that extends infinitely in both directions. It is often described as the shortest distance between any two points. Here, the term "line" is a common shorthand for this object, which is formally called a "straight line" to distinguish it from a curved line.
Definition
In modern mathematics, a line is typically defined as a set of points that satisfies a linear equation. This definition includes lines in any dimension, although in common usage, "line" often refers to a line in a two-dimensional plane.
Properties
A line has several key properties. It is:
- Straight: A line does not curve.
- Infinite: A line extends infinitely in both directions.
- One-dimensional: A line has only one dimension - length.
Line segments and rays
A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points. A ray is a part of a line that has one end point and extends infinitely in one direction.
In Euclidean geometry
In Euclidean geometry, a line is defined as a breadthless length, or the straight path between two points. This is known as the "Euclidean line."
In non-Euclidean geometry
In non-Euclidean geometry, lines can be curved. For example, in spherical geometry, a line is a great circle (the intersection of a sphere with a plane through its center).
