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The operation of taking an nth root of a number.

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within ...