Search Results for ""

A Brocard line is a line from any of the vertices A_i of a triangle DeltaA_1A_2A_3 to the first Omega or second Omega^' Brocard point. Let the angle at a vertex A_i also be ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

In a lattice, any two elements a and b have a least upper bound. This least upper bound is often called the join of a and b, and is denoted by a v b. One can also speak of ...

A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If K=L and h is a join-homomorphism, then we call h a join-endomorphism.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. Then the mapping h is a join-homomorphism provided that for any x,y in L, h(x v y)=h(x) v h(y). It is also ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and onto, then it is a join-isomorphism if it preserves joins.

A lattice L is locally bounded if and only if each of its finitely generated sublattices is bounded. Every locally bounded lattice is locally subbounded, and every locally ...