Polygon geometry definition plus#

Now, let's discuss each of the polygon types.

The types of polygons are listed as follows. The polygons are classified into various types based on the angles and sides. Now, let's discuss the types of a polygon. Similarly, an n-sided polygon is referred to as n-gon. A polygon with atleast three sides is called as triangle and also referred to as 3-gon. To form a closed figure, three line segments need to be joined together. We can say that not all 2D figures are polygons. It is because the circle is a curved shape that does not have any sides or angles. Despite a plane figure, a circle is not considered as a polygon. There is no curve side is present in a polygon. Examples of polygon are triangle, pentagon, hexagon, and many more. The points where line segments are connected are called as corners or vertex. The lines that are used to form a polygon are called as sides or edges. It is formed using a collection of lines. Definition of polygonĪ polygon is defined as a 2D closed geometric figure that has a finite number of sides. The topic is not limited to polygon's definition here, we will also discuss the examples, shapes, types, polygon properties, and some FAQs. 'Polygon.' From MathWorld-A Wolfram Web Resource.In this article, we are going to discuss polygon's definition. Referenced on Wolfram|Alpha Polygon Cite this as: VNRĬoncise Encyclopedia of Mathematics, 2nd ed. Web-Linked Dictionary of Mathematics, 2nd ed. CRC Standard Mathematical Tables, 28th ed. The sum of interior angles in the top left diagram The generalization of a polygon into three dimensions is called a polyhedron, into four dimensions is called a polychoron,Īnd into dimensions is called a polytope. The most familiar type of polygon is the regular polygon, which is a convex polygon with equal sides lengthsĪnd angles. The Greek poly, meaning 'many,' and gonia, meaning 'angle.' If all sides and angles are equivalent, the polygon is called regular. To the area of a triangular lamina when this meaning is clear by context.Ī polygon for which the only points of the plane belonging to two polygon edges ofĪre the polygon vertices is said to be a simple polygon. Will still use imprecise terms such as 'the area of a triangle' to refer However, in keeping with common usage and to avoid excessive verbosity, this work Polygon' to refer to the region of which a closed broken line is the boundary. Perhaps most clear is to use the terms 'polygonal lamina' or 'filled While the 'filled' usage is consistent with common terminology such as 'the area of a square is ,'

Non-filled depending on the number of self-overlaps (see figure above). Polygons are often rendered not as filled, but instead as alternating filled and However, this convention is also not without difficulty, since self-intersecting In computer graphics parlance, the term polygon uniformly refers to a 'filled' polygon, as is the case with the WolframĬommand, where the documentation explicitly includes the word 'filled.' 'closed plane figure' and universally depict polygons as a closed brokenīlack lines with no shading of the interiors.

Polygon geometry definition plus#

Plus the region they enclose, though they never define precisely what is meant by These definitions all imply that a polygon is a set of line segments

2003, p. 137), or 'a closed plane figure boundedīy three or more line segments that terminate in pairs at the same number of vertices,Īnd do not intersect other than at their vertices' (Borowski and Borwein 2005, 'a closed plane figure bounded by straight line segments as its sides' Plane figure with straight edges' (Gellert et al. Other sources commonly define a polygon (in the sense illustrated above) as a 'closed There is unfortunately substantial disagreement over the definition of a polygon. In other words, a polygon is closed broken line lying in a plane' (Coxeter and Greitzer 1967, p. 51). A polygon can be defined (as illustrated above) as a geometric object 'consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points.