Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

Definition

Of an angle

The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.

Of a polytope

A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.

In a polygon, a vertex is called "convex" if the internal angle of the polygon, that is, the angle formed by the two edges at the vertex, with the polygon inside the angle, is less than π radians ( 180°, two right angles) ; otherwise, it is called "concave" or "reflex". More generally, a vertex of a polyhedron or polytope is convex if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and concave otherwise.

Principal

Principal may refer to:

Education & organized religion

Law

Places

Film and TV

Other uses

Vertex

Vertex (Latin: peak; plural vertices or vertexes) may refer to:

Mathematics and computer science

Physics

Biology and anatomy

Companies

Del

Del, or nabla, is an operator used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, dot product, and cross product, respectively, of the del "operator" with the field. These formal products do not necessarily commute with other operators or products.

Segura

Segura (Spanish: [seˈɣuɾa], Valencian: [seˈɣuɾa]; Latin: Thader, Arabic: شقورة, War-Alabiat) is a medium-sized river in southeastern Spain. It has its source in the Sierra de Segura.

Course

The river begins at Santiago Pontones (province of Jaén), passes Calasparra, Cieza, Murcia, Beniaján, Orihuela, Rojales and ends in the Mediterranean Sea near Guardamar del Segura in the province of Alicante. Some of its tributaries are the Mundo (which starts near Riópar), the Alhárabe (which starts in Moratalla), the Mula and the Guadalentín.

The alluvial plain is called the Vega del Segura and is a very productive agricultural region growing a wide variety of fruit, vegetables and flowers. The Vegas are divided into three areas: Alta, Media and Baja (upper, medium, and lower).

Recovery

By the 1990s, the Segura had become one of the most polluted rivers in Europe, due to the canning industry and urban and agricultural residues originating in the densely populated area in the medium and lower areas of the basin. This fact combined with low or extreme low flows in the same areas –the agricultural use of water and summer drought could reduce the mean discharge to just around 2 to 3 m³/s in Murcia city– made more difficult to dilute pollutants.