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A number that is "close" to (but not equal to) zero may be called an almost zero. In contrast, a number or expression that is equal to zero is said to be identically zero. ...

A point x in a manifold M is said to be nonwandering if, for every open neighborhood U of x, it is true that phi^nU intersection U!=emptyset for a map phi for some n>0. In ...

Let phi be a map. Then phi is expansive if the statement that the distance d(phi^nx,phi^ny)<delta for all n in Z implies that x=y. Equivalently, phi is expansive if the ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

One or both of the square bracket symbols [ and ] are used in many different contexts in mathematics. 1. Square brackets are occasionally used in especially complex ...

A random polygon is a polygon generated in some random way. Kendall conjectured that the shape of a random polygon is close to a disk as the area of the polygon becomes large ...