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A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 ...

An estimate is an educated guess for an unknown quantity or outcome based on known information. The making of estimates is an important part of statistics, since care is ...

The Fermat quotient for a number a and a prime base p is defined as q_p(a)=(a^(p-1)-1)/p. (1) If pab, then q_p(ab) = q_p(a)+q_p(b) (2) q_p(p+/-1) = ∓1 (3) (mod p), where the ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by hav(z) = 1/2vers(z) (1) = 1/2(1-cosz) (2) = sin^2(1/2z), (3) where ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...