In geometry, the **line element** or **length element** can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parameterizing the given curve by Frenet–Serret formulas. As such, a *line element* is then naturally a function of the metric, and can be related to the curvature tensor. It is usually denoted by *s* or *ℓ*, and differentials of this are then written *ds* or *dℓ*.

Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved manifold with a metric. For example, if a massive object causes some curvature in spacetime, the trajectory of an object with negligible mass over that curvature would follow the line element according to the geodesic equation.

### Other articles related to "line element, line, lines":

**Line Element**s in 4d Spacetime - General Spacetime

... The coordinate-independent definition of the square of the

**line element**ds in spacetime is In terms of coordinates where for this case the indices α and β run over 0, 1, 2, 3 for spacetime ...

... Central

**Line**is the imaginary

**line**in the middle of each

**line**or

**line element**which is a constitutive part of a graphic character set ... If we consider d as the width of the

**line element**and h as the height of the

**line element**, then the two standard ratios for d/h are 1/14 and 1/10, which are feasible because they result in a minimum number of

**line**... Location of Central

**Lines**- The nominal size (h) and the spacing between characters (a) shall be taken as the basis for defining the central

**line**...

... congruence is stationary, we can imagine replacing each world

**line**in this congruence by a point ... To see this, consider the Born

**line element**Setting ds2 = 0 and solving for dt we obtain The elapsed proper time for a roundtrip radar blip emitted by a ... To do this, we need only integrate our

**line element**over the appropriate null geodesic track ...

### Famous quotes containing the words element and/or line:

“There is only one *element* that can break the Afrikaner, and that is the Afrikaner himself. It is when the Afrikaner, like a baboon shot in the stomach, pulls out his own intestines. We must guard against that.”

—P.W. (Pieter Willem)

“For a woman to get a rewarding sense of total creation by way of the multiple monotonous chores that are her daily lot would be as irrational as for an assembly *line* worker to rejoice that he had created an automobile because he tightened a bolt.”

—Edith Mendel Stern (1901–1975)