Search Results for ""

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

A formula of first-order logic is in prenex normal form if it is of the form Q_1x_1...Q_nx_nM, (1) where each Q_i is a quantifier forall ("for all") or exists ("exists") and ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

The second Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_2=sum_((i,j) in E(G))d_id_j, where E(G) is the edge set of G.

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

The silver constant is the algebraic number given by S = (x^3-5x^2+6x-1)_3 (1) = 2+2cos(2/7pi) (2) = 3.246979603... (3) (OEIS A116425), where (P(x))_n denotes a polynomial ...

A spatial point process is a point process which models data that is localized at a discrete set of locations in space or, more specifically, on a plane.