The Line reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

# Line

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The word line apparently derives from the Latin linum, meaning flax plant from which linen is produced; at one time, a stretched linen thread was the most reliable way to determine a straight line. Also see liner and lining.

The word line can refer to a queue area.

The word line can also mean a line of written, printed or spoken text.

Line is also the name of an obsolete unit of measurement, equal to one-twelfth of an imperial inch.

## Electrical engineering

In electrical engineering, a line is, more generally, any circuit (or loop) of an electrical system. This electric circuit loop (or electrical network), consists of electrical elements (or components) connected directly by conductor terminals to other devices in series.

In telecommunications, a telephone line is a single-user circuit on a telephone communications system.

## Straightness

Depending on context line may mean straight line, or also curve ("curved line"). To avoid confusion the former is usually applicable in mathematical texts, while in graphics, such as drawing, a line may well be curved.

## Mathematics

A line, or straight line, is, roughly speaking, an (infinitely) thin, (infinitely) long, straight geometrical object, i.e. a curve that is long and straight. Given two points, one can always find exactly one line that passes through the two points; the line provides the shortest connection between the points. Three or more points that lie on the same line are called collinear. Two different lines can intersect in at most one point; two different planes can intersect in at most one line. This intuitive concept of a line can be formalized in various ways.

If geometry is developed axiomatically (as in Euclid's Elements and later in David Hilbert's Foundations of Geometry), then lines are not defined at all, but characterized axiomatically by their properties. "Everything that satisfies the axioms for a line is a line." While Euclid did define a line as "length without breadth", he did not use this rather obscure definition in his later development.

In Euclidean space Rn (and analogously in all other vector spaces), we define a line L as a subset of the form

where a and b are given vectorss in Rn with b non-zero. The vector b describes the direction of the line, and a is a point on the line. Different choices of a and b can yield the same line.

One can show that in R2, every line L is described by a linear equation of the form

with fixed real coefficients a, b and c such that a and b are not both zero. Important properties of these lines are their slope, x-intercept and y-intercept.

More abstractly, one usually thinks of the real line as the prototype of a line, and assumes that the points on a line stand in a one-to-one correspondence with the real numbers. However, one could also use the hyperreal numbers for this purpose, or even the long line of topology.

The "straightness" of a line, interpreted as the property that it minimizes distances between its points, can be generalized and leads to the concept of geodesics on differentiable manifolds.