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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.
By considering the connectivity of these neighboring vertices, a vertex figure can be constructed for each vertex of a polytope: Each vertex of the vertex figure coincides with a vertex of the original polytope. Each edge of the vertex figure exists on or inside of a face of the original polytope connecting two alternate vertices from an ...
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University.His main professional expertise was in computational geometry, [2] but he was also a jazz drummer, [3] held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher ...
Modulation is sometimes said to be problematic for shape-note systems, since the shapes employed for the original key of the piece no longer match the scale degrees of the new key; [5] but the ability to use of sharp and flat symbols along with shape notes is a matter of the range of sorts available to the typographer and musical preferences.
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.
Vertex (geometry), a point where two or more curves, lines, or edges meet; Vertex (computer graphics), a data structure that describes the position of a point; Vertex (curve), a point of a plane curve where the first derivative of curvature is zero; Vertex (graph theory), the fundamental unit of which graphs are formed
An endpoint of a segment is called a vertex (plural: vertices) [2] or a corner. Edges and vertices are more formal, but may be ambiguous in contexts that also involve the edges and vertices of a graph; the more colloquial terms sides and corners can be used to avoid this ambiguity. [4] The number of edges always equals the number of vertices. [2]