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What is a polygon?
A polygon is a planar figure defined by a limited number of straight line segments joined to create a closed polygonal chain in geometry (or polygonal circuit). A polygon can be specified as a bounding circuit, a bounded planar area, or both.
The segments are the edges or sides of a polygonal circuit. The vertices (singular: vertex) or corners of a polygon are the spots where two edges meet. A solid polygon’s interior is sometimes referred to as its body. A polygon with n sides is called an n-gon; for example, a triangle is a 3-gon.
A simple polygon is one that has no points that intersect. Mathematicians are frequently just interested in the bounding polygonal chains of basic polygons, and they define a polygon in this way. Star polygons and other self-intersecting polygons can be created when a polygonal boundary is allowed to cross over itself.
A polygon is a two-dimensional representation of the polytope, which can have any number of dimensions. There are many more polygon generalizations defined for various reasons.
Polygons on mathematics
Polygons are a frequent introduction to fundamental geometry and mathematics in primary education. Children quickly grasp the concept of a polygon and love learning the names of different polygon forms. The use of toy pieces encourages even toddlers to learn about polygons. Polygons are crucial to the study of geometry, and understanding them provides a strong basis for middle school math.
Classification
Convexity and intersection
The convexity or non-convexity of polygons can be characterized as follows:
Any line traced through the polygon that is not tangent to an edge or corner crosses its boundary twiceAs a result, none of the inner angles are more than 180°. Any line segment with boundary endpoints travels through only interior locations between its endpoints, or vice versa.
Non-convex: a line that encounters its border more than twice can be discovered. Between two border points that travel outside the polygon, or vice versa, a line segment occurs.
Equality and symmetry
Equiangular means that all corner angles are the same.
Equilateral means that all of the edges are the same length.
Equilateral and equiangular regularity.
A single circumcircle connects all four corners, making it cyclic.
All edges of an inscribed circle are tangent to it.
All corners of the symmetry orbit are isogonal or vertex-transitive. In addition, the polygon is cyclic and equiangular.
All sides of the symmetry orbit are isotoxal or edge-transitive. The polygon is also tangential and equilateral.
How Polygons are Used in Daily Life Situations
Real life applications of polygons are:
The squared form of the tiles you walk on indicates that they are polygons.
The truss of a construction or bridge, the walls of a building, and so on are all polygons. The trusses are triangular, whereas the walls are rectangular.
A polygon is the rectangular portion of a chair on which you are seated.
A polygon is the rectangular-shaped screen on your laptop, television, or mobile phone.
A polygon is an example of a rectangular football pitch or playground.
The Bermuda Triangle is a polygon with a triangle form.
Polygons may also be seen in Egypt’s Pyramids (triangular)
A polygon is a figure with a star form.
Polygons can also be found on road signs.
- A polygon is a modeling and rendering primitive in computer graphics.
Examples of Polygons
Let’s take an example how to make polygons,
John has a square of paper in his hand. He wants to cut the paper into two more polygons of the same size and shape (other than rectangles). Provide alternatives.
Solution:
There are two ways to cut a rectangular piece of paper so that he receives two more polygons of the same size and form (but aren’t rectangles):
He can cut two squares of the same size and form from a rectangle piece of paper by cutting vertically from the middle.
He can make two triangles of the same size and shape by cutting a rectangular sheet of paper diagonally.
Importance of Polygons
The variety of polygon forms commonly used in the construction of modern constructions would most likely explain their relevance. Because of its reasonably strong design, the triangle is commonly used in construction. The usage of the polygon form minimizes the amount of resources used to construct a structure, lowering costs and increasing profits in a corporate setting. The rectangle is another polygon. Because our field of view is predominantly rectangular, the rectangle is used in a variety of applications. Most televisions, for example, are rectangular to make watching easier and more enjoyable. Photo frames and phone screens are in the same boat.
Also see: CAT Previous Year Papers
Conclusion
A simple polygon is one that has no points that intersect. Mathematicians are frequently just interested in the bounding polygonal chains of basic polygons, and they define a polygon in this way. When a polygonal boundary is permitted to cross over itself, star polygons and other self-intersecting polygons can be generated. A polygon is a two-dimensional representation of a more general object that can have any number of dimensions. There are many more polygon generalizations defined for various reasons.
