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A parabola, one of the simplest curves, after (straight) lines. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.
Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. In a sense, [a] all lines in Euclidean geometry are equal, in that, without coordinates, one can not tell them apart from one another. However, lines may play special roles with respect to other objects in the geometry and be divided into types ...
Toggle Generally composed of straight line segments subsection. 1.1 Polygons with specific numbers of sides. 2 Curved. Toggle Curved subsection. 2.1 Composed of ...
A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm. In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
This is equivalent to saying that they are birational to the product of a curve and a projective line. Sometimes a ruled surface is defined to be one satisfying the stronger condition that it has a fibration over a curve with fibers that are projective lines. This excludes the projective plane, which has a projective line though every point but ...
In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the shortest [a] path between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the ...
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints.