Cynthia Lanius

Polyominoes -

Perimeter

The perimeter of polyominoes is another interesting investigation. Complete the following table on the perimeter of the polyominoes.

No. of Squares Perimeter
1
  
    
2
  
    
    
3
  
    
    
    
&
    
    
    

Think you see a pattern here? So can you predict what the perimeter of the tetrominoes (4 squares) is?

No. of Squares Perimeter
4
    

    
    
    
    
   
    
    
    
    
    
    
    
    
    
    
    
    
    
   
   

Was your prediction correct? Did you predict that there would be two different perimeters? (?!) A word of caution: be careful with predictions. Sometimes a function will vary from the particular pattern it begins with.

Let's make another table and label the perimeters minimum and maximum. After you complete the table, graph the ordered pairs as points on a coordinate plane. Make two graphs, letting x represent No. of Squares and y represent both the minimum and maximum perimeters.

No. of Squares Minimum Perimeter Maximum Perimeter
1    
2    
3    
4    
5    
6    
7    
8    
9    

Challenge Problem: Find the curve of best fit for both the long and short perimeters.

Next: Polyominoes On the Web


Go to - Next || Previous || Main || Teachers' Notes

lanius@math.rice.edu
Copyright 1998-2004 Cynthia Lanius URL http://math.rice.edu/~lanius/Lessons/Polys/poly6.html