Search Results for ""

The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

A knot diagram is a picture of a projection of a knot onto a plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

Let P, Q be integers satisfying D=P^2-4Q>0. (1) Then roots of x^2-Px+Q=0 (2) are a = 1/2(P+sqrt(D)) (3) b = 1/2(P-sqrt(D)), (4) so a+b = P (5) ab = 1/4(P^2-D) (6) = Q (7) a-b ...

A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above ...

Every position of every impartial game has a nim-value, making it equivalent to a nim-heap. To find the nim-value (also called the Sprague-Grundy number), take the mex of the ...

The norm of a mathematical object is a quantity that in some (possibly abstract) sense describes the length, size, or extent of the object. Norms exist for complex numbers ...

A polygonal number of the form n(3n-1)/2. The first few are 1, 5, 12, 22, 35, 51, 70, ... (OEIS A000326). The generating function for the pentagonal numbers is ...

The sequence of Fibonacci numbers {F_n} is periodic modulo any modulus m (Wall 1960), and the period (mod m) is the known as the Pisano period pi(m) (Wrench 1969). For m=1, ...