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The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

The Cesàro means of a function f are the arithmetic means sigma_n=1/n(s_0+...+s_(n-1)), (1) n=1, 2, ..., where the addend s_k is the kth partial sum ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

An epsilon-delta definition is a mathematical definition in which a statement on a real function of one variable f having, for example, the form "for all neighborhoods U of ...

The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...