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Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. Tangent plane to a sphere. In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems , and play an important role in many geometrical constructions and proofs .
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
The dimension of the tangent space at every point of a connected manifold is the same as that of the manifold itself. For example, if the given manifold is a -sphere, then one can picture the tangent space at a point as the plane that touches the sphere at that point and is perpendicular to the
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R n. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of ...
For any closed subvariety X in a projective space, the set of all hyperplanes tangent to some point of X is a closed subvariety of the dual of the projective space, called the dual variety of X. Examples. If X is a hypersurface defined by a homogeneous polynomial F(x 0, ..., x n), then the dual variety of X is the image of X by the gradient map
Since this image is meant as a replacement to [[:Image:Tangent.png]], which was deleted as a result, I assume that this image, just as that one, is released under GFDL. 2007-04-28 21:10 Jacj 400×280 (3195 bytes) A labelled tangent to a curve.
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. Three given circles generically have eight different circles that are tangent to them and each solution circle encloses or excludes the three given circles in a different way: in each solution, a different subset of the ...
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