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In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. [1] This is typically a local maximum or minimum of curvature, [ 2 ] and some authors define a vertex to be more specifically a local extremum of curvature. [ 3 ]
A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. 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. [1] [2] [3]
In mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights associated to the edges.
Draw an angle whose vertex is point V and whose sides pass through points A, B. Draw line OA. Angle ∠BOA is a central angle; call it θ. Lines OV and OA are both radii of the circle, so they have equal lengths. Therefore, triangle VOA is isosceles, so angle ∠BVA (the inscribed angle) and angle ∠VAO are equal; let each of them be denoted ...
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory.In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.
The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on. The sum of the external angles of any simple polygon, if only one of the two external angles is assumed at each vertex, is 2π radians (360°).
Given this information, the degree-sum formula can be used to recover the number of edges in the given graph and the degrees of each vertex. From this, it is possible to determine whether the given graph is a regular graph , and if so to determine it uniquely from any vertex-deleted subgraph by adding a new neighbor for all the subgraph ...