Difference between revisions of "Tessellation Exploration: The Basics"

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{{Exploration}}
 
{{Exploration}}
 
{{Time|45}}
 
{{Time|45}}
{{Objective| Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.}}
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{{Objective|Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.}}
  
 
==Tessellations by Triangles and Quadrilaterals==
 
==Tessellations by Triangles and Quadrilaterals==
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<li> 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.
 
<li> 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.
  
[[Image:Parallelogram.png|center]]
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[[Image:Parallelogram.png|center|300px]]
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<li> Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
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<li> 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.
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<li> Why does this imply that all triangles will tessellate the plane?
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==Tessellations of the Plane by Regular Polygons==
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A {{define|regular tessellation}} is a tessellation made of regular, congruent, convex 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.
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<li> What is the common name for a regular 3-gon?
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<li> What is the common name for a regular 4-gon?

Revision as of 12:34, 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.


  5. What is the common name for a regular 3-gon?
  6. What is the common name for a regular 4-gon?