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Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

The n-pan graph is the graph obtained by joining a cycle graph C_n to a singleton graph K_1 with a bridge. The n-pan graph is therefore isomorphic with the (n,1)-tadpole ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Sudoku (literally, "single number"), sometimes also is a pencil-and-paper logic puzzle whose goal is to complete a grid satisfying various constraints. In the "classic" ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...

If r is a root of the polynomial equation x^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, where the a_is are integers and r satisfies no similar equation of degree <n, then r is called an ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

B-trees were introduced by Bayer (1972) and McCreight. They are a special m-ary balanced tree used in databases because their structure allows records to be inserted, ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...