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The tangent line to a point on a differentiable curve can also be thought of as a tangent line approximation, the graph of the affine function that best approximates the original function at the given point. [3] Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the
The tangential angle φ for an arbitrary curve A in P. In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the x-axis. [1] (Some authors define the angle as the deviation from the direction of the curve at some fixed starting point.
Development can be generalized further using flat connections. From this point of view, rolling the tangent plane over a surface defines an affine connection on the surface (it provides an example of parallel transport along a curve), and a developable surface is one for which this connection is flat.
As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the ...
In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space in higher dimensions. In the context of physics the tangent space to a manifold at a point can be viewed as the space of possible velocities for a particle moving on ...
In particular, the tangent plane to a point of S can be rolled on S: this should be easy to imagine when S is a surface like the 2-sphere, which is the smooth boundary of a convex region. As the tangent plane is rolled on S, the point of contact traces out a curve on S. Conversely, given a curve on S, the tangent plane can be rolled along that ...
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 ...
The geodesic curvature k g at a point of a curve c(t), parametrised by arc length, on an oriented surface is defined to be [58] = ¨ (). where n(t) is the "principal" unit normal to the curve in the surface, constructed by rotating the unit tangent vector ċ(t) through an angle of +90°.