Matches Polyominoes

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Matches- Polyominoes

• Laura Ryan and Sam ONeill

2
Investigation

• Polyominoes- Investigate the numbers of matches
  needed to make others
• This shape is a polyominoe
  constructed using matchsticks.

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Polyominoes

• Polyominoes are figures formed of congruent
  squares placed so that the squares have a common
  side.
• A three squared shape is called a triomino.
• A four squared Polyominoe is called a tetrominoe.
  

The red line indicates the common side shared for
each square.
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Algebraic Equation for Polyominoes.

• 3n1m
• Where n number of squares and m number of
  matches.
• This equation will work as long as each square is
  connected to one square.
• To add six squares, ___ number of matches are
  needed.
• Using the equation the answer is
• 3 x 6 1 19
• Therefore, 19 matches are needed for six squares.

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Shapes

• By changing the order of the matches, it is
  possible to make different shapes with the same
  amount of matches used.
• These shapes still feature the common side found
  in polyominoes, still contain the same number of
  matches and boxes as the original shape.
• These are common shapes found in the Tetris game.
  

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Investigation one
A pattern was noticed where number of matches- in
the ones place value was 7, 2 recurring. In the
tens place value- the first value was repeated
eg- 1,1, 2, 2, 3, 3.
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Investigation two
A pattern was noticed in the number of matches
in the ones place value, the pattern was 7, 3, 9,
5, 1, 7, 3 this was repetitious as the same
number of matches was added.
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Findings from investigation

• Whilst the number of Boxes stayed constant in
  both investigations, the number of matches
  changed in each.
• Between the two investigations, the number of
  matches in investigation one increased by five
  and in investigation two, the number of matches
  increased by six.

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Angles

• Polyominoes have sixteen angles within the shape.
  There are four angles per box. Each angle in the
  square is equal to 90 degrees which is a right
  angle. These angles add up to a total of 1440
  degrees.

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How many matches

• By adding or subtracting matches, you are able to
  change the shape.
• By adding four more matches to the shape, six
  boxes are created.
• Upon doing this, the shape is then not recognised
  as a Polyominoe. Though, by adding six more
  matches, three to each side, as shown, the shape
  is still recognised as resembling a polyominoe,
  has the common side feature as the polyominoe but
  does not have the same amount of matches needed.

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Boundaries

• Through this investigation we discovered that
  even though we were adding 5 matches each time,
  the boundary was only increasing by 2.
• This was because we were only adding to the
  height of the shape and the other 3 matches
  became common inside sides.

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Excel spreadsheet working
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Common Use of Polyominoes

• You will Find Polyominoe shapes used in the game
  of Tetris. The aim of this game is trying to
  place the different Polyominoe shapes together so
  there is no gaps.
• Click here to play Tetris http//math.rice.edu/
  lanius/Lessons/Polys/tetris/neave_tetris.html