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The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...

The incidence matrix of a graph gives the (0,1)-matrix which has a row for each vertex and column for each edge, and (v,e)=1 iff vertex v is incident upon edge e (Skiena ...

The inverse cosine is the multivalued function cos^(-1)z (Zwillinger 1995, p. 465), also denoted arccosz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 307; ...

The Lagrange interpolating polynomial is the polynomial P(x) of degree <=(n-1) that passes through the n points (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n)), and ...

The Lovász number theta(G) of a graph G, sometimes also called the theta function of G, was introduced by Lovász (1979) with the explicit goal of estimating the Shannon ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

Multivariate zeta function, also called multiple zeta values, multivariate zeta constants (Bailey et al. 2006, p. 43), multi-zeta values (Bailey et al. 2006, p. 17), and ...