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When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

Consider the consecutive number sequences formed by the concatenation of the first n positive integers: 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and ...

Ramanujan calculated mu=1.45136380... (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is mu=1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114). The ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

A triangle center (sometimes simply called a center) is a point whose trilinear coordinates are defined in terms of the side lengths and angles of a triangle and for which a ...