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A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

A regularly spaced array of points in a square array, i.e., points with coordinates (m,n,...), where m, n, ... are integers. Such an array is often called a grid or mesh, and ...

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

An accumulation point is a point which is the limit of a sequence, also called a limit point. For some maps, periodic orbits give way to chaotic ones beyond a point known as ...

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...

In general, the catacaustics of the astroid are complicated curves. For an astroid with parametric equations x = cos^3t (1) y = sin^3t, (2) the catacaustic for a radiant ...