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Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

Catastrophe theory studies how the qualitative nature of equation solutions depends on the parameters that appear in the equations. Subspecializations include bifurcation ...

Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

Let p be a non-wandering point of a diffeomorphism S:M->M of a compact manifold. The closing lemma concerns if S can be arbitrarily well approximated with derivatives of ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

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 ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...