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Pre-Calculus

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The Bailey mod 9 identities are a set of three Rogers-Ramanujan-like identities appearing as equations (1.6), (1.8), and (1.7) on p. 422 of Bailey (1947) given by A(q) = ...

Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A? The ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

In continuum percolation theory, the Boolean-Poisson model is a Boolean model driven by a stationary point process X which is a Poisson process. The Boolean-Poisson model is ...

The simple continued fraction representations for Catalan's constant K is [0, 1, 10, 1, 8, 1, 88, 4, 1, 1, ...] (OEIS A014538). A plot of the first 256 terms of the continued ...