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The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates to 1650 BC. It was purchased by Henry Rhind in Egypt in 1858, and placed in the British ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...