Cynthia Lanius

Polyominoes -

Investigation

Polyominoes can be organized by their number of squares. Examine the table below.

No. of Squares
1
    
2
    
    
3
    
    
    
&
    
    
    

 

Notice that there is only one way to make a figure with one or two squares, but there are two ways to form a triomino. As we saw earlier, there are 5 different tetrominoes (4 squares).

No. of Squares
   
    
    
    
    
    
    
    
4
    
    
    
    
    
    
    
    
    
    
   
   

 
Now one other thing you need to know - a reflection, rotation or translation of a piece is not a different piece. For example, the two pieces below are the same piece, just flipped over. For more on transformations see Types of Symmetry In the Plane by Susan Addington and Suzanne Alejandre.

    
    
    
  
    
    
    
    
    

 

Assignment: Exploration
Pentominoes are polyominoes with 5 squares. How many different pentominoes would there be? Explore by drawing them on square grid paper. You may print out this grid paper if you need it.

 

Next: see the pentominoes


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