Polyominoes

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Polyominoes

• Hilary Yeomans

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Investigation Question

• Polyominoes are made up of a number of squares
  connected by common sides. Thirteen matches
  where used to make this one with four squares.
  Investigate the number of
  matches needed
  to make others.

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Discussion of Task

• Lines and boxes how many matches are used to
  make different shapes?
• Discussed the direction of investigation

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Research

• I researched Polyominoes on the internet and
  found some information that changed the direction
  of our investigation.
• Exactly What are Polyominoes?
• Different Kinds of Polyominoes
• Formulas

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Exactly What are Polyominoes?

• Polyominoes are figures formed of congruent
  squares placed so that the squares share a side
• Domino and Tetris pieces are examples of
  polyominoes
• A reflection, rotation or translation of a
  polyomineo is not a different piece.

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Different Kinds of Polyominoes

• There are different types of Polyominoes.
  Polyominoes can be organized by their number of
  squares.
• Triominoes - Made up of 3 boxes
• Tetrominoes - Made up of 4 boxes
• Pentominoes - Made up of 5 boxes
• Hexominoes - Made up of 6 boxes
• Septominoes Made up of 7 boxes
• And so on

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Formulas
1
4
3
1
2
2
5
3
6
4
3
7
3
10
(n - 1)
4
4
3
(n - 1)
3
3
4
4
3
(3 - 1)
x 2
4
3
4
6
10
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A New Direction

• We shouldn't just focus on boxes and lines, but
  other shapes as well.
• How many different Polyominoes can we come up
  with without rotating or flipping?

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Conclusion

• The nature of this investigation limited the
  depth of our research. We had difficulty finding
  other areas to look into.
• This PowerPoint presentation has been included in
  the curriculum and knowledge section of my
  e-portfolio

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References

• Cynthia Lanius Lesson Polyominoes Introduction
  http//math.rice.edu/lanius/Lessons/Polys/poly1.
  html
• Hakmem Polyominoes http//www.inwap.com/pdp10/hbak
  er/hakmem/polyominos.html
• Math World http//mathworld.wolfram.com/Polyomino.
  html