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If the Tutte polynomial T(x,y) of a graph G is given by sumt_(rs)x^ry^s, then the matrix (t_(rs)) is called the rank matrix of G. For example, the Tutte matrix of the ...

A cube whose edge lengths are 1. The unit cube therefore has unit volume.

A disk with radius 1. The (open) unit disk can also be considered to be the region in the complex plane defined by {z:|z|<1}, where |z| denotes the complex modulus. (The ...

The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

Algebra

A method for constructing magic squares of odd order, also called the Siamese method.

A k-matrix is a kind of cube root of the identity matrix (distinct from the identity matrix) which is defined by the complex matrix k=[0 0 -i; i 0 0; 0 1 0]. It satisfies ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...