Cutting Rectangles Into Two Identical Pieces

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Cutting Rectangles Into Two
Identical Pieces

• Amanda MacLean
• Tim Tarrant

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Our QuestionCUTSMake a rectangular grid of
squares. Cut it along the grid lines to make two
identical pieces.

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Example 1
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Example 2
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Example 3
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Example 4
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Our Rectangles

• For each rectangle we allowed each square within
  the rectangle to have a value of 1 unit.
• For example

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The Area of the Rectangles

• The formula to find the area of rectangles is
• Length (l) Breadth (b).

Example
Length
Breadth
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Our Examples

• For each of our example rectangles the area must
  equal an even number
• so that it can be cut into two identical pieces.

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• Amandas Findings

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Example 1

• When ever the length is even the rectangle can be
  cut into identical pieces in this way. The value
  of the breadth does not affect how it can be
  cut..

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Example 2

• Even length combined with uneven breadth allows
  the rectangle to be cut into 2 identical pieces.

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• Timothys Findings

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Example 3

• To be able to cut a rectangle in this way the
  breadth must be one less then length for example
• Breadth equally 4 Length equally 3
• - 12

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Example 3

• When the Length is equal to or greater than 3, we
  found that the rectangle with the area equal to
• l(l-1)
• With l standing for length.

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Example 3

• For example
• 18 (18-1) 306

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Example 3

• For example
• 30 (30-1) 870

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Example 4

• For this rectangle to be cut evenly the breadth
  needs to be even, the length can be any whole
  number measurement odd or even.

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Our Findings

• When the rectangle has an even area, it allows us
  to cut it in 4 different ways. For example we can
  cut a rectangle when
• the length and breadth are both even.
• the length is even and the breadth is odd the
  rectangle can still be cut into 2 even amounts
  because the area remains even.

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Our Findings

• The examples we found can not be cut into
  identical pieces when
• the length and breadth are both odd numbers,
  because this would give the rectangle an area of
  an odd number, therefore we can not cut it into 2
  identical pieces.

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Conclusion

• We found that there were many different
  contributing factors which effect the ways a
  rectangle can be cut into 2 identical pieces. The
  main contributing factor is the area of the
  rectangle.
• Thanks
• Manda Tim