REGULAR MOSAICS
Section: Geometry
 
TesSELLATING THE PLANE WITH REGULAR POLYGONS 
Regular mosaics are those formed when the only shape used to cover the plane is a regular polygon and where each vertex in the mosaic is a vertex where one of the polygons meets another.

1.- Find out which regular polygons can be used in a regular mosaic. Try to explain what you find out by referring to (a) the size of the interior angles of a regular polygon and (b) the fact that each vertex needs to connect with three or more other tiles to cover a complete angle (360º).

 

2.-If you haven't been able to do the previous activity, work out which numbers divide exactly into 360º and check which ones are equal to the interior angle of a regular polygon. For example, we know that the interior angle of a regular hexagon is 120º and 120º divides exactly into 360º. Therefore, a regular hexagon can be used to form a regular mosaic.

The three regular polygons that tessellate the plane are: equilateral triangles, squares and regular hexagons.

3.- Prove that the above statement is true using these three windows to show that the above shapes will tessellate the plane completely, regardless of the size of the tile. 

  

Point A is fixed. Move point B to change the size of the shape.

 
       
           
  Ángel Aguirre Pérez - aap@sauron.quimica.uniovi.es
 
Spanish Ministry of Education. Year 2001
 
 

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