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A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

Anomalous cancellation is a "canceling" of digits of a and b in the numerator and denominator of a fraction a/b which results in a fraction equal to the original. Note that ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

Let J be a finite group and the image R(J) be a representation which is a homomorphism of J into a permutation group S(X), where S(X) is the group of all permutations of a ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

For any prime number p and any positive integer n, the p^n-rank r_(p^n)(G) of a finitely generated Abelian group G is the number of copies of the cyclic group Z_(p^n) ...