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The arts of Mathematics

TESSELLATIONS

A Tessellation or Tiling is the process of covering a surface with a pattern of flat shapes so that there are no gaps or overlaps.

Here are some examples:

       

 

Regular Tessellations

Are those made of the repetition of these three regular polygons:

Squares        Hexagons   and Equilateral triangles  

There are only 3 regular tessellations:

 

To name a tessellation you have to count how many sides each polygon has and also look at the corner point of each figure -the vertex- and count the number of figures that meet there.

Semi-regular tessellations

Are made of two or more regular polygons. So now you do not see the same figure repeated all the time but a combination of two or more.

 

In the first example we can see a combination of octogons and squares. In the second example there are triangles and dodecagons.

Question 1. For the figures above, is the pattern the same at each vertex?

Other tessellations

Other more complex tessellations can be made of irregular polygons or other shapes such as circles, animals, etc.

Have a look at these tessellations:

  

There are lots of different tessellations. Now let's focus on this geometric art in real life

Tessellations in Real Life

We live surrounded by things that are tessellated. Can you think of some?

Let's see some examples:

  

A brick wall, a honeycomb or a pavement are simple examples of tessellations in everyday life.

Question 2. Can you name the type of tessellation of each example?

But maybe one of the most interesting examples of tessellation is the decoration of walls in the Islamic architecture.

La Alhambra in Granada (Spain) is a beautiful illustration of that.

  

And another reference of this artistic expression is the Dutch artist M.C. Escher whose visits to La Alhambra inspired his work.

  

Impressive, isn't it?

Now, have a look at this short video where you can learn how to create your own tessellation. 

 

Whay don't you try creating your own tessellation? You may need a pair of compasses, a ruler, a rubber, pencil, sellotape and some colour pencils.

When you have finished, try answering the multiple-choice test.

Short url:   https://multidict.net/cs/2756