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Mathematics LibreTexts

2. Regular Tilling

This page is a draft and is under active development. 

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Goal: To appreciate polygons and support the idea that there are three regular polygons that be tessellated.

Terminology:

  • A polygon is a closed 2-dimensional figure with straight sides

    • An n-gon is a polygon with exactly n sides

    • A regular n-gon is a polygon with exactly n sides, where all sides are of equal length and all interior angles of the polygon are equal. The sum of the interior angles of a regular n-gon is 180°(n - 2). It follows that each interior angle must measure 180°(n - 2)/n. So:

      • A regular 3-gon is an equilateral triangle. Each interior angle is 60°

      • A regular 4-gon is a square. Each interior angle is 90°

      • A regular 5-gon is a regular pentagon. Each interior angle is 108°

      • A regular 6-gon is a regular hexagon. Each interior angle is 120°

      • A regular 7-gon is a regular heptagon. Each interior angle is 900/7°, or approximately 128.6°

      • A regular 8-gon is a regular octagon. Each interior angle is 135°

Activity:

Suppose I want to tape the same regular n-gons together to make 2-dimensional shapes. What are my options? I don’t want to bend or fold the n-gons. Let’s just concentrate on the corners of these objects.

Fact:


This page titled 2. Regular Tilling is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Pamini Thangarajah.

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