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Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. [1] Curved spaces can generally be described by Riemannian geometry , though some simple cases can be described in other ways.
A space curve is a curve for which is at least three-dimensional; a skew curve is a space curve which lies in no plane. These definitions of plane, space and skew curves apply also to real algebraic curves, although the above definition of a curve does not apply (a real algebraic curve may be disconnected).
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
A space-filling curve's approximations can be self-avoiding, as the figures above illustrate. In 3 dimensions, self-avoiding approximation curves can even contain knots. Approximation curves remain within a bounded portion of n-dimensional space, but their lengths increase without bound. Space-filling curves are special cases of fractal curves ...
This is a list of Wikipedia articles about curves used in different fields: ... Space-filling curve (Peano curve) See also List of fractals by Hausdorff dimension.
Just as space and time are different aspects of a more comprehensive entity called spacetime, mass–energy and momentum are merely different aspects of a unified, four-dimensional quantity called four-momentum. In consequence, if mass–energy is a source of gravity, momentum must also be a source.
A plane curve with non-vanishing curvature has zero torsion at all points. Conversely, if the torsion of a regular curve with non-vanishing curvature is identically zero, then this curve belongs to a fixed plane. The curvature and the torsion of a helix are constant. Conversely, any space curve whose curvature and torsion are both constant and ...
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. [1] Peano's curve is a surjective, continuous function from the unit interval onto the unit square, however it is not injective. Peano was motivated by an earlier result of Georg Cantor that these two sets have the same ...