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An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

The inverse cotangent is the multivalued function cot^(-1)z (Zwillinger 1995, p. 465), also denoted arccotz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...

A cyclic group is a group that can be generated by a single element X (the group generator). Cyclic groups are Abelian. A cyclic group of finite group order n is denoted C_n, ...