tantalising tessellations everybody knows that squares tessellate. what exactly is meant by this?
TRANSCRIPT
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Tantalising Tessellations
Everybody knows that squares tessellate.
What exactly is meant by this?
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A tessellation originally was the result of covering an area
with tesserae – the small square blocks used by the Romans to make mosaics.
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Nowadays the word tessellation is used to
represent any ‘tiling’ of a plane surface by a regular pattern of one or more congruent,
non-overlapping shapes
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This is a tessellation
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This is not a tessellation
Can you spot the odd tiles out?
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This is not a tessellation
Can you spot the odd tiles out?
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Can you show that a tessellation can be
made from any parallelogram?
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If you can think of parallelograms forming strips, you can also see that they fit together
very easily.
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Can you show that a tessellation can be
made from any triangle?
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If you think of it, a parallelogram can
be made from two triangles.
Finding other patterns could be more
worthwhile.
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How would you show that no tessellation is
possible from a regular pentagon?
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The 108o
corners cannot be fitted together to form 360o
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The 108o
corners cannot be fitted together to form 360o
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It stands to reason then that if the corners do
not add up to 360o the shapes will not
tessellate.
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The fact is …
only three regular shapes will tessellate
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The equilateral triangle
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The square
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The regular hexagon
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The regular hexagon
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Extensions
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Extension 1
Do all pentagons with one pair of parallel lines tessellate?
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Extension 2
Are there other pentagons which tessellate?
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
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Extension 2
The second quadrilateral was obtained by rotating
the first through 180o about O, the midpoint of a
side.
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Extension 2
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Extension 2
Keep doing this and you will soon see a tessellation of quadrilaterals
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Extension 3
Try the method used in Extension 2 for re-
entrant quadrilaterals such as …
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Extension 3
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Extension 3
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Extension 3
Why does this method always work?