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The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the ...

Given a polynomial p(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 (1) of degree n with roots alpha_i, i=1, ..., n and a polynomial q(x)=b_mx^m+b_(m-1)x^(m-1)+...+b_1x+b_0 (2) of ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...