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Diagonal - Polygons | | Diagonal - Polygons: Encyclopedia II - Diagonal - Polygons | | As applied to a polygon, a diagonal is a line segment joining two vertices that are not adjacent. Therefore a quadrilateral has two diagonals, joining opposite pairs of vertices. For a convex polygon the diagonals run inside the polygon. This is not so for re-entrant polygons. In fact a polygon is convex if and only if the diagonals are internal.
When n is the number of vertices in a polygon and d is the number of possible different diagonals, each vertex has possible diagonals to all other vertices save for itsel ...
See also:Diagonal, Diagonal - Polygons, Diagonal - Matrices, Diagonal - Geometry | | | Diagonal, Diagonal - Geometry, Diagonal - Matrices, Diagonal - Polygons, diagonal matrix, main diagonal | | |
| | | Diagonal: Encyclopedia II - Diagonal - Polygons
Diagonal - Polygons
As applied to a polygon, a diagonal is a line segment joining two vertices that are not adjacent. Therefore a quadrilateral has two diagonals, joining opposite pairs of vertices. For a convex polygon the diagonals run inside the polygon. This is not so for re-entrant polygons. In fact a polygon is convex if and only if the diagonals are internal.
When n is the number of vertices in a polygon and d is the number of possible different diagonals, each vertex has possible diagonals to all other vertices save for itself and the two adjacent vertices, or n-3 diagonals; this multiplied by the number of vertices is
(n − 3) × n,
which counts each diagonal twice (once for each vertex) — therefore,
Other related archivesBetti numbers, Cartesian product, Elementary mathematics, Euler characteristic, Lefschetz fixed point theorem, circle, convex polygon, diagonal matrix, equivalence class, fixed points, identity matrix, line segment, main diagonal, mapping, mathematics, matrix, polygon, quadrilateral, re-entrant polygons, subset, torus, vector fields
 Adapted from the Wikipedia article "Polygons", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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