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Published byKeyon Clover Modified over 2 years ago

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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 108 o corners cannot be fitted together to form 360 o

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It stands to reason then that if the corners do not add up to 360 o 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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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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The second quadrilateral was obtained by rotating the first through 180 o about O, the midpoint of a side.

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Extension 2

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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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Why does this method always work?

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