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Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...