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The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

The cubitruncated cuboctahedral graph is the skeleton of the cubitruncated cuboctahedron, which is the only uniform polyhedron for which this is the case. It is illustrated ...

Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

A number n is said to be divisible by d if d is a divisor of n. The function Divisible[n, d] returns True if an integer n is divisible by an integer d. The product of any n ...

Down arrow notation is an inverse of the Knuth up-arrow notation defined by evn = lnn (1) evvn = ln^*n (2) evvvn = ln^(**)n, (3) where ln^*n is the number of times the ...

The sum of powers of even divisors of a number. It is the analog of the divisor function for even divisors only and is written sigma_k^((e))(n). It is given simply in terms ...