Polygon Power

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By jwblackwell

Quiz

Flashcards

9 Questions

What is a polygon?

What are the segments of a closed polygonal chain called?

What is an n-gon?

What is a regular polygon?

What is the shoelace formula used for?

What is the Bolyai-Gerwien theorem?

What is a polygon mesh?

What is the point in polygon test used for?

What are some applications of polygons?

Summary

Polygon Definition and Properties

  • A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

  • The segments of a closed polygonal chain are called edges or sides, and the points where two edges meet are the polygon's vertices or corners.

  • Polygons are primarily classified by the number of sides, and an n-gon is a polygon with n sides.

  • A polygon may be simple, meaning it does not intersect itself, or self-intersecting, creating star polygons and other non-simple shapes.

  • A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

  • The word polygon derives from the Greek adjective πολύς (polús) 'much', 'many' and γωνία (gōnía) 'corner' or 'angle'.

  • Polygons may be characterized by their convexity or type of non-convexity, such as a concave polygon.

  • A polygon is regular if and only if it is both isogonal and isotoxal, or equivalently it is both cyclic and equilateral.

  • The area of a simple polygon can be calculated using the shoelace formula or surveyor's formula.

  • For any two simple polygons of equal area, the Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon.

  • The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p.

  • The coordinates of the centroid of a solid simple polygon are calculated using a formula that incorporates the signed value of the area.

  • Individual polygons are named and classified according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, such as pentagon and dodecagon.Polygons: Definition, Examples and Applications

  • Polygons are two-dimensional geometric shapes consisting of straight lines that form a closed shape.

  • The study of non-convex polygons was first carried out by Thomas Bradwardine in the 14th century.

  • Polygons have been generalized to the complex plane by Geoffrey Colin Shephard in 1952.

  • Polygons appear in nature, such as in rock formations and the wax honeycomb made by bees.

  • Regular hexagons can occur when lava cools and forms tightly packed columns of basalt.

  • In computer graphics, polygons are used as primitives for modeling and rendering.

  • Any surface is modeled as a tessellation called a polygon mesh, which is a collection of polygons.

  • The imaging system renders polygons in correct perspective for viewing on a display system.

  • The point in polygon test is used in computer graphics and computational geometry to determine whether a given point lies inside a polygon.

  • Polygons have a wide range of applications, including in computer graphics, architecture, and engineering.

  • Understanding polygons is important for geometry, trigonometry, and other fields of mathematics.

  • The study of polygons continues to evolve, with new applications and techniques being discovered all the time.

Description

Test your knowledge of polygons with this informative quiz! From their definition and properties to real-life applications and interesting facts, this quiz covers everything you need to know about polygons. Challenge yourself and see how well you know this important geometric shape.

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