2. Objective: Students will… (1) Understand the concept of and the process of making tessellations. (2) Create tessellations using: Rotation, Translation, Reflection (3) Understand the works of M. C. Escher. (4) Use elements and principles of design: color, balance, repetition and pattern. (5) Use the skills they have learned to produce a UNIQUE tessellation of their own Please read the entire PowerPoint before beginning.

3. Who is famous for tessellations? A man who is famous for his art work with tessellation was Maurits Cornelis Escher, from Leeuwarden, Netherlands. The picture on the right is his self-portrait. A man who is famous for his art work with tessellation was Maurits Cornelis Escher, from Leeuwarden, Netherlands. The picture on the right is his self-portrait. He said, “My work is a game, a very serious game.” He said, “My work is a game, a very serious game.”

4. M. C. Escher Most famous creator of tessellations Most famous creator of tessellations Born in Holland in 1898 (died in 1972) Born in Holland in 1898 (died in 1972) Originally studied architecture before becoming interested in woodcuts and printmaking Originally studied architecture before becoming interested in woodcuts and printmaking Did 137 tessellations in his lifetime Did 137 tessellations in his lifetime

5. M. C. Escher Among his greatest admirers were mathematicians, who recognized in Escher’s work an extraordinary visualization of mathematical principles. This was quite remarkable as Escher had no formal mathematics training beyond secondary school.

6. Tessellations by M.C. Escher

7. Famous Tessellations This is one of Escher’s most famous tessellations. It is simply called “Reptiles” This is one of Escher’s most famous tessellations. It is simply called “Reptiles”

8. Bulldog (Tessellation 97)

9. Pegasus (Tessellation 105)

10. Lizard (Tessellation 104)

11. *Three Common Transformations *1. Translation, which is a slide of the polygon. *2. Reflection, which is a flip or mirror image of the polygon. *3. Rotation, which is a turn around one vertex of the polygon. Transformation are an important part of creating tessellations.

12. Transformations Geometric shapes can be translated, reflected, rotated, or glide reflected. Geometric shapes can be translated, reflected, rotated, or glide reflected. These movements of the shapes create a more interesting tessellation design. These movements of the shapes create a more interesting tessellation design. Translation Rotation Reflection Glide Reflection

13. Tessellations, or regular divisions of the plane, are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are polygons or similar regular shapes (like square tiles used on floors). Escher exploited these basic patterns in his tessellations, applying reflections, translations, and rotations to obtain a greater variety of patterns. He also “distorted” these shapes to form animals, birds, and other figures. These distortions had to obey the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation. Tessellations, or regular divisions of the plane, are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are polygons or similar regular shapes (like square tiles used on floors). Escher exploited these basic patterns in his tessellations, applying reflections, translations, and rotations to obtain a greater variety of patterns. He also “distorted” these shapes to form animals, birds, and other figures. These distortions had to obey the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation.

14. Materials: 3 index cards to make 3 (3x3) squares 3 index cards to make 3 (3x3) squares Pencil Pencil Scissors Scissors Markers, crayons or colored pencils Markers, crayons or colored pencils Poster board Poster board Piece of construction paper Piece of construction paper Create Your Own Tessellation

15. First Make a Template !

16. Translations - a slide

18. Reflections - mirror images Watch this video: http://www.youtube.com/watch?v=QR0uK5PRzRQ

19. Glide Reflections

20. Rotations - turns

22. Seeing a Figure Looking at your tessellation template, study the sides and the shape to decide what sort of figure you might see. Looking at your tessellation template, study the sides and the shape to decide what sort of figure you might see. The person who designed this form saw an elephant and an elf. The person who designed this form saw an elephant and an elf. Are there any other different forms that you might see? Are there any other different forms that you might see? When looking for the shape be sure not to see too much detail as it can make the art work too crowded. When looking for the shape be sure not to see too much detail as it can make the art work too crowded.

23. Putting It All Together Take your tessellation template and trace it on to a piece of paper. Take your tessellation template and trace it on to a piece of paper. When tracing you can use different types of symmetry to change your picture. When tracing you can use different types of symmetry to change your picture. Be sure that your whole page is filled with a repeating pattern. Be sure that your whole page is filled with a repeating pattern. Color in your picture creatively. Color in your picture creatively. Elephants Translation symmetry Elves and Elephants Combinations of symmetry

24. http://www.tessellations.org/tess-symmetry2.shtml http://teacherweb.com/MD/CentennialHS/MrStephenLee/Tessellations---Glide-Reflections.pdf http://www.youtube.com/watch?v=Lc4LGZwlcvs Check out these websites for more information on how to make a tessellation… http://www.youtube.com/watch?v=ynHQU9rFlhg

25. Enjoy making your own tessellations! So, as you can see, tessellations are fun to learn about and easier to make than perhaps, you originally thought. So, as you can see, tessellations are fun to learn about and easier to make than perhaps, you originally thought.