Lesson plan
Line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc length, is a function of the metric tensor and is denoted by ds . Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved pseudo-Riemannian manifold with an appropriate metric tensor.
Article summary
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc length, is a function of the metric tensor and is denoted by ds . Line elements are used in physics, especially in theories of gravitation (most notably general relativity) where spacetime is modelled as a curved pseudo-Riemannian manifold with an appropriate metric tensor.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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