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A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.
Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. Definition [ edit ]
For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [1] [2] [3]
Note that changing F into –F would not change the curve defined by F(x, y) = 0, but it would change the sign of the numerator if the absolute value were omitted in the preceding formula. A point of the curve where F x = F y = 0 is a singular point, which means that the curve is not differentiable at this point, and thus that the curvature is ...
A plane simple closed curve is also called a Jordan curve. It is also defined as a non-self-intersecting continuous loop in the plane. [9] The Jordan curve theorem states that the set complement in a plane of a Jordan curve consists of two connected components (that is the curve divides the plane in two non-intersecting regions that are both ...
Note that a p-circular curve must have degree at least 2p. The set of p-circular curves of degree p + k, where p may vary but k is a fixed positive integer, is invariant under inversion. [citation needed] When k is 1 this says that the set of lines (0-circular curves of degree 1) together with the set of circles (1-circular curves of degree 2 ...
Examples of circular motion include: special satellite orbits around the Earth (circular orbits), a ceiling fan's blades rotating around a hub, a stone that is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a ...
This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ...