Search Results for ""

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...

The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...