Convex polygon

Convex Polygon A simple polygon is a finite region of the plane bounded by a non-self-sealing closed broken line. Taking into account how a simple polygon is with respect to a line that contains two of its points, two classes of polygons result: convex polygons and concave polygons.

Summary

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  • 1 Definition
    • 1 Examples
  • 2 elements
    • 1 Topological concepts
  • 3 Features
  • 4 Sources
  • 5 References
  • 6 See also

Definition

A polygon is convex when a line that contains any of its sides determines two half planes, such that in one of them the whole polygon remains; in case no such property occurs the polygon “is not convex”. [one]

Examples

  • Triangles
  • Square, rectangle, rhombus, rhomboid, trapezoid and trapezoids.
  • Pentagons, hexagons, octagons, enegons, decagons, hexagons, dodecagons, etc.

Elements

  • Side of the polygon is any segment of the broken line
  • Vertex any end of one side, this vertex on two sides called adjacent
  • Diagonal: Any segment that joins two non-consecutive vertices.
  • From the vertex of an entering angle, a decomposition into convex figures with a smaller number of sides is possible, if possible into triangles.

Topological concepts

  • Inner point of a convex polygon. If we draw any line through point I that cuts two sides of the polygon at M and N respectively, if I is between M and N it is an interior pointof the polygon.
  • Interior: It is the set of all interior points.
  • Polygonal region: It is the union of the polygon and its interior.
  • Border is the broken line that delimits the polygon.
  • Exterior point: It is a point that is not in the polygonal region. The set of all exterior points is the exteriorof the polygon.
  • The interior, exterior and polygon establish a plane partition, so that the intersection of two of them is empty and the union of the three sets is equal to the entire plane.
  • Accumulation point of a polygon Π is a point P athat has an environment V (P a  ; δ) so that it contains at least one point Π other than P a .
  • Isolated point of a polygon K is a point P ithat is in K and that has an environment V (P i  ; δ), which does not contain any point of K, outside it.

characteristics

  1. In a convex polygon all its diagonals are on the same polygon; otherwise they are inside except for the ends that are on the border.
  2. Any two different points on the polygon determine a segment that is on the polygon.
  3. If a line is drawn through an interior point, it is cut at least two of its sides.
  4. Three-sided polygons ( triangles) are the only polygons that cannot be concave, since none of their three angles can exceed 180 degrees or π radians.

 

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