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The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

The lower central series of a Lie algebra g is the sequence of subalgebras recursively defined by g_(k+1)=[g,g_k], (1) with g_0=g. The sequence of subspaces is always ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

The lituus is an Archimedean spiral with n=-2, having polar equation r^2theta=a^2. (1) Lituus means a "crook," in the sense of a bishop's crosier. The lituus curve originated ...

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

The Maltese cross is a symbol identified with the Christian warrior whose outward points form an octagon (left figure). Another class of cross sometimes (incorrectly) known ...

Mills' constant can be defined as the least theta such that f_n=|_theta^(3^n)_| is prime for all positive integers n (Caldwell and Cheng 2005). The first few f_n for n=1, 2, ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...