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Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

A number n for which the harmonic mean of the divisors of n, i.e., nd(n)/sigma(n), is an integer, where d(n)=sigma_0(n) is the number of positive integer divisors of n and ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...

Half of a sphere cut by a plane passing through its center. A hemisphere of radius r can be given by the usual spherical coordinates x = rcosthetasinphi (1) y = ...

The hyperbolic cylinder is a quadratic surface given by the equation (x^2)/(a^2)-(y^2)/(b^2)=-1. (1) It is a ruled surface. It can be given parametrically by x = asinhu (2) y ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

Suppose x_1<x_2<...<x_n are given positive numbers. Let lambda_1, ..., lambda_n>=0 and sum_(j=1)^(n)lambda_j=1. Then ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...