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The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

An n×n Latin square is a Latin rectangle with k=n. Specifically, a Latin square consists of n sets of the numbers 1 to n arranged in such a way that no orthogonal (row or ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place. For example, the only derangements of {1,2,3} are {2,3,1} and ...