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Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

The term domain has (at least) three different meanings in mathematics. The term domain is most commonly used to describe the set of values D for which a function (map, ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

Consider an arbitrary one-dimensional map x_(n+1)=F(x_n) (1) (with implicit parameter r) at the onset of chaos. After a suitable rescaling, the Feigenbaum function ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...