Search Results for ""

The downward Clenshaw recurrence formula evaluates a sum of products of indexed coefficients by functions which obey a recurrence relation. If f(x)=sum_(k=0)^Nc_kF_k(x) (1) ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

A method for solving ordinary differential equations using the formula y_(n+1)=y_n+hf(x_n,y_n), which advances a solution from x_n to x_(n+1)=x_n+h. Note that the method ...

Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent, ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...