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The finite difference is the discrete analog of the derivative. The finite forward difference of a function f_p is defined as Deltaf_p=f_(p+1)-f_p, (1) and the finite ...

The floor function |_x_|, also called the greatest integer function or integer value (Spanier and Oldham 1987), gives the largest integer less than or equal to x. The name ...

Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

In a 1847 talk to the Académie des Sciences in Paris, Gabriel Lamé (1795-1870) claimed to have proven Fermat's last theorem. However, Joseph Liouville immediately pointed out ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...