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The M'Cay cubic Z(X_3) is a self-isogonal cubic given by the locus of all points whose pedal circle touches the nine-point circle, or equivalently, the locus of all points P ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...

The multiplicad is a simple example of an idea like the ruliad. It consists of a rulial multiway system based on the positive integers in which the rules simply multiply by ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

Let (A,<=) and (B,<=) be disjoint totally ordered sets with order types alpha and beta. Then the ordinal sum is defined at set (C=A union B,<=) where, if c_1 and c_2 are both ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...