Line

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).

See also

• Point (geometry)
• Plane (geometry)
• Curve
• Angle

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