In combinatorics, a vertex is another name for a node.

--back to combinatorics--

A parabola has one vertex: it is the point of greatest curvature, and it is usually considered to be the centre of the parabola. For graphs of the form y = (ax - b)2 + c, the vertex is at (b/a, c). If a is positive, this is the lowest point on the graph, if a is negative, this is the highest point.

The vertex of a parabola is the only point which is both on the parabola and on the parabola's axis of symmetry.

A hyperbola has two vertices. Again, these are the points of maximum curvature, and they also lie on an axis of symmetry (hyperbolae have two axes of symmetry, but one of them does not touch either curve). They are the two points, one on each 'side' of the hyperbola, which are closest to each other.

Stretching the definition, the two points of greatest curvature on an ellipse may also be considered vertices. These points are on the major axis, the two points on the ellipse which are farthest from each other. This is a rare usage of the word, however.

Ver"tex (?), n.; pl. Vertexes (#), L. Vertices (#). [L. vertex, -icis, a whirl, top of the head, top, summit, from vertere to turn. See Verse, and cf. Vortex.]

A turning point; the principal or highest point; top; summit; crown; apex.

Specifically: --

(a) Anat.

The top, or crown, of the head.

(b) Anat.

The zenith, or the point of the heavens directly overhead.

(c) Math.

The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base.

⇒ The principal vertex of a conic section is, in the parabola, the vertex of the axis of the curve: in the ellipse, either extremity of either axis, but usually the left-hand vertex of the transverse axis; in the hyperbola, either vertex, but usually the right-hand vertex of the transverse axis.

Vertex of a curve Math., the point in which the axis of the curve intersects it. -- Vertex of an angle Math., the point in which the sides of the angle meet. -- Vertex of a solid, ∨ of a surface of revolution Math., the point in which the axis pierces the surface.


© Webster 1913.

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