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The intersection of two lines L_1 and L_2 in two dimensions with, L_1 containing the points (x_1,y_1) and (x_2,y_2), and L_2 containing the points (x_3,y_3) and (x_4,y_4), is ...

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 ...

An 80-sided polygon.

One of the eight regions of space defined by the eight possible combinations of signs (+/-,+/-,+/-) for x, y, and z.

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The point at which a curve or function crosses the x-axis (i.e., when y=0 in two dimensions).

The point at which a curve or function crosses the y-axis (i.e., when x=0 in two dimensions).

Let phi_0 be the latitude for the origin of the Cartesian coordinates and lambda_0 its longitude, and let phi_1 and phi_2 be the standard parallels. Then for a unit sphere, ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

The term "Cartesian" is used to refer to anything that derives from René Descartes' conception of geometry (1637), which is based on the representation of points in the plane ...