© T Madas. 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.

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Presentation transcript:

© T Madas

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?

© 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 ?

© 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.

© 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

© T Madas triangles, squares and hexagons

© T Madas triangles, squares and hexagons

© T Madas

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

© T Madas

Tessellations can be made using all sorts of shapes

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

© T Madas This is where Mathematics meets Art

© T Madas Maurits Cornelius Escher The most famous mathematical artist is the Dutchman, Escher

© T Madas

another tessellating pattern

© T Madas