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The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. ...

There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

If a random variable X has a chi-squared distribution with m degrees of freedom (chi_m^2) and a random variable Y has a chi-squared distribution with n degrees of freedom ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

Subresultants can be viewed as a generalization of resultants, which are the product of the pairwise differences of the roots of polynomials. Subresultants are the most ...