Search Results for ""

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

A number of the form aba..., abab..., etc. The first few nontrivial undulants (with the stipulation that a!=b) are 101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, ... ...

The uniformity conjecture postulates a relationship between the syntactic length of expressions built up from the natural numbers using field operations, exponentials, and ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...