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Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

Origami is the Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...