Difference between revisions of "Escher-Like Tessellations Explorations"

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1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.)  
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1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!
  
 
[[Image:Parallellogram-net.png]]
 
[[Image:Parallellogram-net.png]]
 
   
 
   
2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.)
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2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!
  
 
[[Image:Diamond-net.png]]
 
[[Image:Diamond-net.png]]
 
   
 
   
3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex.
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3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. Make sure you create a tessellation with a recognizable figure!
  
 
[[Image:Square-net.png]]
 
[[Image:Square-net.png]]
 
   
 
   
 
   
 
   
4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations  through  the midpoints.
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4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations  through  the midpoints. Make sure you create a tessellation with a recognizable figure!
  
 
[[Image:Hexagon-net.png]]
 
[[Image:Hexagon-net.png]]

Revision as of 12:04, 23 July 2007


Time-45.svg

Objective: Escher developed his tessellations from the more primitive geometric tessellations using isometries. We will practice several of the techniques that will create an Escher-like tessellation.


1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

Parallellogram-net.png

2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

Diamond-net.png

3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. Make sure you create a tessellation with a recognizable figure!

Square-net.png


4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations through the midpoints. Make sure you create a tessellation with a recognizable figure!

Hexagon-net.png


Handin: A sheet with answers to all questions.