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A rose curve, also called Grandi's rose or the multifolium, is a curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

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) ...

Given a Taylor series f(z)=sum_(n=0)^inftyC_nz^n=sum_(n=0)^inftyC_nr^ne^(intheta), (1) where the complex number z has been written in the polar form z=re^(itheta), examine ...

Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The ...

The anticomplement of a point P in a reference triangle DeltaABC is a point P^' satisfying the vector equation P^'G^->=2GP^->, (1) where G is the triangle centroid of ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has ...