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The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

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 ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and Schrijver ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...