Five Times The Fun

1
Five Times The Fun

• A power point presentation on Polyominoes and
  Pentominoes

2
Polyominoes

• Made with adjacent squares that share a common
  edge.
• 1 square Monomino, 2 Domino, 3
  Triomino, 4 Tetromino, 5
  Pentomino,
• Mainly used for recreational purposes.
• We will focus on Pentominoes

3
PENTOMINO MANIA

• Pentominoes are made of 5 squares, each sharing
  at least 1 common edge with another square.
• Each arrangement of squares is labled with the
  letter it looks like.
• They became famous in the 1950s and have kept
  mathematicians busy as they continually find new
  things they can do.

4
Fun With Pentominoes

• There are many challenging puzzles that can be
  done with pentominoes.
• There are over 2,339 ways to arrange the
  petominoes in a 6x10 grid.
• This is one way ?

5
What is so special about these squares?

• 60 squares in a set of Pentominoes.
• The set has the ability to completely cover a
  square with out any overlap or holes.
• If there is a cube with that has an edge of 10
  units, Pentominoes can cover it completely with
  only one of each piece.
• If we bend the pieces, it is even possible to
  fit all 12 pieces onto a sphere with out any
  overlap.
• If you are looking for formulas on polyominoes
  and pentominoes, then this is the site to check
  out!

6
Pentominoes make the Cube!
7
Applications???

• Pentominoes are not all fun and games.
• Art and Design are a major area where polyominoes
  and pentaminoes are used.
• When laying tile on a floor or wall, different
  patterns of polyominoes are also used.

8
Why are they important?

• Pentominoes should be taught in school for a
  couple of very important reasons.
• Pentominoes are fairly new, only being discovered
  in 1953, but they are a fun way to get students
  to think spatially and develop the ability to do
  mental flips and rotations in their heads.
• They also show kids that just because you have a
  different answer, it is not necessarily wrong.
• Teaching pentominoes can easily tie into other
  areas of math like perimeter, area, symmetry, and
  tessalations.

9
What Next?

• As of now, most of what Pentominoes are is simply
  puzzles.
• However, these puzzles can come to reveal
  patterns that apply to more than just these
  suqares.
• Research on Pentominoes and Polyominoes is
  ongoing.
• Mathematicians and scientists are exploring more
  ways that these unique sets of squares affect our
  lives.