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In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false. In statistics, a hypothesis (sometimes called a ...

Let M be a bounded set in the plane, i.e., M is contained entirely within a rectangle. The outer Jordan measure of M is the greatest lower bound of the areas of the coverings ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...

Given a sequence S_i as input to stage i, form sequence S_(i+1) as follows: 1. For k in [1,...,i], write term i+k and then term i-k. 2. Discard the ith term. 3. Write the ...

The Minkowski metric, also called the Minkowski tensor or pseudo-Riemannian metric, is a tensor eta_(alphabeta) whose elements are defined by the matrix (eta)_(alphabeta)=[-1 ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...

The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have ...

A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number ...