Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

2. Regular Tessellation

[ "stage:draft", "article:topic", "authorname:thangarajahp", "license:ccbysa", "showtoc:yes" ]
  • Page ID
    13597
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    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: