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A principal vertex x_i of a simple polygon P is called an ear if the diagonal [x_(i-1),x_(i+1)] that bridges x_i lies entirely in P. Two ears x_i and x_j are said to overlap ...

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

Let p and q be partitions of a positive integer, then there exists a (0,1)-matrix A such that c(A)=p, r(A)=q iff q is dominated by p^*.

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

An analytic function approaches any given value arbitrarily closely in any epsilon-neighborhood of an essential singularity.

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...