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Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

Consider the Euclid numbers defined by E_k=1+p_k#, where p_k is the kth prime and p# is the primorial. The first few values of E_k are 3, 7, 31, 211, 2311, 30031, 510511, ... ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

Consider the recurrence relation x_n=(1+x_0^2+x_1^2+...+x_(n-1)^2)/n, (1) with x_0=1. The first few iterates of x_n are 1, 2, 3, 5, 10, 28, 154, ... (OEIS A003504). The terms ...

A Moiré pattern is an interference pattern produced by overlaying similar but slightly offset templates. A simple example is obtained by taking two identical ruled ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...