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A Cauchy surface is a subset of a region in space-time, which is intersected by every non-spacelike, inextensible curve exactly once. In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... In the context of special relativity, space-like separated points (or events) in spacetime have a spacetime interval less than 0 (see sign convention). ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
In 1833 the deposed king Charles X of France summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made.
Returning to Paris in 1838, Cauchy refused a proffered chair at the Collège de France, but in 1848, the oath having been suspended, he resumed his post at the École Polytechnique, and when the oath was reinstituted after the coup d'état of 1851, Cauchy and François Arago were exempted from it.
Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847, and a judge of the court of cassation in 1849; and Eugène François Cauchy (1802–1877), a publicist who also wrote several mathematical works.
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