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Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

Cards are a set of n rectangular pieces of cardboard with markings on one side and a uniform pattern on the other. The collection of all cards is called a "deck," and a ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

Let X be a set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A in V(X) be a finitary algebra with finitely many fundamental operations. Then ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...