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, line element, lines":

... 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 ... 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**...

**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 ...

... the Langevin 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:

“The *element* running through entire nature, which we popularly call Fate, is known to us as limitation. Whatever limits us, we call Fate.”

—Ralph Waldo Emerson (1803–1882)

“If surrealism ever comes to adopt a particular *line* of moral conduct, it has only to accept the discipline that Picasso has accepted and will continue to accept.”

—André Breton (1896–1966)