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Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

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 ...

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 ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

A Lie algebra is a vector space g with a Lie bracket [X,Y], satisfying the Jacobi identity. Hence any element X gives a linear transformation given by ad(X)(Y)=[X,Y], (1) ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence of a set containing all the natural numbers, exists x(emptyset in x ^ forall y in x(y^' in x)), where ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

A catenary of revolution. The catenoid and plane are the only surfaces of revolution which are also minimal surfaces. The catenoid can be given by the parametric equations x ...