Polygonal line

Polygonal line . The geometric elements segment and angles , with which others that are proper subsets of the plane will be formed, specifically plane figures that are not linear. Firstly, flat figures will be considered that are sets formed by two or more consecutive segments.

Summary

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  • 1 Plane Geometry
  • 2 Symbolic expression
  • 3 Classification of traverse
  • 4 Sources

Plane geometry

The part of geometry that is dedicated to the study of plane figures is called Plane Geometry or Planimetry . The polygonal line is a flat figure formed by a set of segments, located one after the other, so that each two of them are joined by a common end.

Symbolic expression

Applying the given definition, we have the following symbolic expression: let A1 A2…, AN be different points on the plane, then the union set: A1 A2 A3…., AN = A1 A2 U A2 A3 U…. U AN-1 AN is called a traverse line or more briefly a traverse line. The elements of the traverse are side (each segment), vertex (common ends of two consecutive segments), ends (uncommon ends on two sides).

Polygonal classification

The traverse can be classified according to different criteria. I. Whether they have ends or not: if they have ends, polygonal open; if they do not have ends, polygonal closed.

Open polygon line

Closed polygon line

  1. Whether or not the traverse is on the same half plane with respect to a line that contains any of its sides.
  2. a) Convex polygonal is one that is located on the same semi-plane with respect to the linethat contains any of its sides.
  3. b) Concave polygonal is one that is located in different semi-planes with respect to at least one of the lines that it contains on either side.

Every closed polygonal line determines a partition in the set of points of the plane, that is, disjoint subsets are formed. One of the subsets is the traverse line itself and the remaining subsets can be distinguished by whether or not they contain lines. The subset that does not contain lines is called the inner region and the subset that does contain lines is called the outer region. In different books, the polygonal line is named by the term broken line, if you analyze the given definition and the illustrated representatives, you can see that the term broken gives a clear idea of ​​the corresponding concept.

 

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