1. Using Transformations to Create Fantastic Tessellations! Dr. Maria Mitchell 1

2. What is a Tessellation? 2

3. The graphic artist M.C. Escher (1898 – 1972) was intrigued with the idea of creating a single shape that could be copied and then used to cover a surface without any gaps or overlaps. These coverings or tilings of the plane are called TESSELLATIONS. 3

4. M.C. Escher 4

5. M.C. Escher Creations http://www.mcescher.com/ http://www.teachers.ash.org.au/geparker/exa mples_of_tessellations.htm http://www.teachers.ash.org.au/geparker/exa mples_of_tessellations.htm 5

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9. Explore Shapes that Tile the Plane 9

10. Interactive Pattern Blocks http://illuminations.nctm.org/ActivityDetail.aspx?id=202 http://illuminations.nctm.org/ActivityDetail.aspx?id=202 10

11. Moves Used to Make the Tilings 11

12. Transformations Translation 12

13. Nibbling 13

14. Simple Translation Tessellation Polygon should have opposite sides that are parallel and congruent. squares hexagons parallelograms 14

15. Transformations Reflection 15

16. Glide Reflection Tessellation Polygon should have opposite sides that are parallel and congruent. squares hexagons parallelograms 16

17. Transformations Rotation 17

18. Rotational Tessellation Adjacent sides must be congruent. squares triangles hexagons parallelograms 18

19. Now You Can Make Your Electronic Tessellation Using Pattern Blocks http://illuminations.nctm.org/ActivityDetail.as px?id=202 http://illuminations.nctm.org/ActivityDetail.as px?id=202 19

20. Now You Can Make Your Electronic Tessellation Using Microsoft Paint http://www.teachers.ash.org.au/geparker/creating_a_basic_tessellation_using_microso ft_paintbrush.htm 20