Difference between revisions of "Tessellation Exploration: The Basics"

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<li> Why does this imply that all triangles will tessellate the plane?  
 
<li> Why does this imply that all triangles will tessellate the plane?  
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</ol>
  
 
==Tessellations of the Plane by Regular Polygons==
 
==Tessellations of the Plane by Regular Polygons==
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A {{define|semi-regular tessellation}} is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.
 
A {{define|semi-regular tessellation}} is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.
  
 
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<ol|start=4>
 
<li> What is the common name for a regular 3-gon?
 
<li> What is the common name for a regular 3-gon?
  
 
<li> What is the common name for a regular 4-gon?
 
<li> What is the common name for a regular 4-gon?

Revision as of 12:36, 18 May 2007


Time-45.svg

Objective: Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.

Tessellations by Triangles and Quadrilaterals

  1. Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page.
    Parallelogram.png
  2. Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
  3. Draw an acute, an obtuse and a right triangle. Now convince yourself of the fact that two congruent copies of the same triangle fit together to form a parallelogram or a rectangle.
  4. Why does this imply that all triangles will tessellate the plane?

Tessellations of the Plane by Regular Polygons

A regular tessellation is a tessellation made of regular, congruent, convex polygons.


A semi-regular tessellation is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.

<ol|start=4>

  • What is the common name for a regular 3-gon?
  • What is the common name for a regular 4-gon?