What is a Polygon

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A basic understanding of polygons is required to analyze shapes, find areas, and perform geometric equations. In this article, you will learn about the definition, types, properties, as well as practical use cases of polygons. Many of them, basic geometrical ingredients — polygons — are fundamental shapes that is used in many fields: mathematics, architecture, engineering, computer graphics.

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Polygon

A polygon is a closed 2D shape formed by finite line segments connected to form a closed chain or polygonal circuit. The term "polygon" is derived from the Greek word which translates to "many angles," with 'poly' meaning "many" and 'gon' meaning "angles."

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Features of Polygons:

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Closed Shape: All of a polygon's sides must connect for it to be a closed figure.

Straight Sides: Curved lines do not form polygons; they are made up entirely of straight-line segments.

Two-dimensional: Polygons have length, breadth, and no depth in a flat plane.

Three Sides: A triangle with three sides is the most basic polygon.

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Polygon examples include:

• Triangle with three sides
• A quadrilateral with four sides
• Pentagon (five sides)
• Hexagon with six sides
• Octagon with eight sides

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Types Of Polygon

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Polygons can be classified by several characteristics, such as the number of sides, edges, angles, or symmetry.

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1. According to the Number of sides

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• Triangle: A three-sided polygon.
• A polygon having four sides is called a quadrilateral.
• The Pentagon is also a polygon with five sides.
• Hexagon: A polygon with six (6) sides.
• Heptagon: A polygon with seven sides.
• Octagon: A polygon with eight sides.

2. Based on Regularity

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• The angles and side lengths are equal in a regular polygon like a square or an equilateral triangle.
• A scalene triangle or an irregular pentagon is an irregular polygon with its angles and side lengths mismatched.

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3. Convexity-based

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• Additionally, in all convex polygons, internal angles can only measure less than 180 degrees, while at least one internal angle of a concave polygon will measure more than 180 degrees.
• Concave Polygon: A reverse indentation is when one internal angle of a polygon is greater than 180 degrees.

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4. Based on Complexity

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• A simple polygon does not intersect itself.
• A polygon intersects itself, usually called a complex polygon.

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Properties of Polygons

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Each polygon has its unique attributes based on its type and structure. Among their requisite qualities are:

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1. Sum of Interior Angles

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The sum of a polygon's interior angles is represented as (n-2) x 180°, where n is the number of sides.

For instance:

• A triangle with three sides would be like (n - 2) x 180°

                                                                             (3-2) x 180° = 180°

• A quadrilateral has four sides would be like (4 - 2) x 180°

                                                                             2 x 180° = 360°

• A pentagon has five sides would be like (5 - 2) x 180°

                                                                              3 x 180°= 540°

2. Exterior Angles

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The exterior angles of any polygon always sum to 360 degrees.

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3. Diagonals in a Polygon

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The number of diagonals of a polygon is given by the following formula n (n-3)/2, where n is the number of sides.

For instance;

• Triangle: 3 (3 - 3) / 2 = 0, so it has no diagonal.
• The number of sides in a square is 4, so 4 x (4 - 3) / 2 = 2, or that it has two diagonals.
• The Pentagon has five sides, so 5 (5-3) / 2 = 5, so it has five diagonals.

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Practical Applications of Polygons

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Following are the practical applications of polygon that are used in different fields;  

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1. Engineering and Architecture

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• For the planning of structure, design, and blueprints, polygons are used.
• To enhance the efficiency of floor tiles and make them more aesthetic then, hexagonal patterns are used.

2. Computer Graphics and Gaming

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• Video games and 3D modeling rely on polygons to construct complex objects.
• Triangles and quadrilaterals are used to render wireframe models.

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3. Cartography and Navigation

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• Polygons on geographic maps represent land areas and territories.
• GPS systems use polygons to map boundaries and roadways.

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4. Design and Art

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• Polygons are used in geometric patterns in many creative designs.
• Polygonal shapes are used in tessellation and origami patterns.

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5. Nature and Science

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• Natural hexagons, or honeycombs, maximize efficiency and available space.
• In chemistry, polygonal patterns are frequently formed by molecular structures.

6. Polygons in Robotics and Artificial Intelligence

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Because they serve as the basis for object detection and spatial analysis, polygons are essential in robotics and artificial intelligence (AI). Important uses consist of:

• Computer Vision & AI: To precisely evaluate and categorize objects, AI-driven image recognition systems deconstruct complicated images into polygonal forms.
• Autonomous Navigation: To navigate areas, identify impediments, and choose the best routes, robots employ polygonal mapping techniques.
• 3D Modeling in Robotics: Detailed robotic models for simulations and practical applications are made possible by polygon meshes.
• Facial Recognition: To effectively evaluate and match facial structures, AI-powered facial recognition software uses polygonal mapping.

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Famous Polygons in Mathematics

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Numerous unique polygons are well-known in science and mathematics:

• In an equilateral triangle, all three sides and angles are equal.
• A square is a quadrilateral that has right angles and equal sides.
• A polygon with side ratios that adhere to the golden ratio (1.618) is called a golden rectangle.
• Because they save space, hexagons are frequently found in nature (such as honeycombs).

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Conclusion

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Geometry, engineering, computer graphics, and nature all depend on polygons. Polygons are the building blocks of numerous ideas and concepts, whether they are used in digital art, navigation maps, or architectural constructions. We can better appreciate their function in a variety of sectors and daily life by being aware of their characteristics, classifications, and uses.

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FAQs

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1. Which polygon is the simplest?

With three sides and three angles, a triangle is the most basic polygon.

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2. How is the perimeter of the polygon calculated?

The perimeter for polygons is the sum of its sides, P = s1 + s2 + s3 +.....+sn, where s is the length of the side.

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3. What is the real-life application of polygons?

Polygon corresponds to fundamental elements of structural design and digital modeling in architecture, the computer graphics and mapping disciplines, and various fields within the natural sciences.

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