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2. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not overlap. W h a t i s a t e s s e l l a t i o n?

3. © T Madas A regular tessellation uses identical regular polygons to fill the plane. There are only 3 regular tessellations, using squares, equilateral triangles or regular hexagons. What is a Regular Tessellation ?

4. © T Madas Archimedean Tessellations or semi-regular tessellations These are tessellations using only regular polygons, with two or more different polygons around each vertex with each vertex having the same pattern of polygons round it.

5. © T Madas There are 8 Archimedean Tessellations: triangles and squares triangles and hexagons triangles and dodecagons squares, hexagons and dodecagons squares and octagons triangles, squares and hexagons

6. © T Madas triangles, squares and hexagons

7. © T Madas triangles, squares and hexagons

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9. This tessellation is not regular or semi-regular. Can you explain why?

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12. Tessellations can be made using all sorts of shapes

13. © T Madas Tessellations can be made using all sorts of shapes

14. © T Madas This is where Mathematics meets Art

15. © T Madas Maurits Cornelius Escher 1898-1972 The most famous mathematical artist is the Dutchman, Escher

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38. another tessellating pattern

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