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 a minimum number ... 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. ...

... However, because 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 Langevin observer is then Therefore ... 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:

“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one *element* after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”

—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)

“It is a great many years since at the outset of my career I had to think seriously what life had to offer that was worth having. I came to the conclusion that the chief good for me was freedom to learn, think, and say what I pleased, when I pleased. I have acted on that conviction... and though strongly, and perhaps wisely, warned that I should probably come to grief, I am entirely satisfied with the results of the *line* of action I have adopted.”

—Thomas Henry Huxley (1825–95)