Search Results for ""

A ruled surface M is a tangent developable of a curve y if M can be parameterized by x(u,v)=y(u)+vy^'(u). A tangent developable is a developable surface.

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

A function f(x) has a vertical tangent line at x_0 if f is continuous at x_0 and lim_(x->x_0)f^'(x)=+/-infty.

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

Let (x_0,y_0) be any point of a surface function z=f(x,y). Then the surface has a nonvertical tangent plane at (x_0,y_0) with equation ...

A vector field is a section of its tangent bundle, meaning that to every point x in a manifold M, a vector X(x) in T_xM is associated, where T_x is the tangent space.

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...