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A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

Christoffel symbols of the second kind are the second type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. ...

Define a cell in R^1 as an open interval or a point. A cell in R^(k+1) then has one of two forms, {(x,y):x in C, and f(x)<y<g(x)} (1) or {(x,y):x in C, and y=f(x)}, (2) where ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

A quantity which gives the inclination of a curve or line with respect to another curve or line. For a line in the xy-plane making an angle theta with the x-axis, the slope m ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...

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The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...