Objective: Students will

Transcription

1 Please read the entire PowerPoint before beginning. 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

2 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. He said, My work is a game, a very serious game.

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

4 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.

5 Tessellations by M.C. Escher

6 Famous Tessellations This is one of Escher s most famous tessellations. It is simply called Reptiles

7 Bulldog (Tessellation 97)

8 Pegasus (Tessellation 105)

9 Lizard (Tessellation 104)

10 Transformation are an important part of creating tessellations. *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.

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

12 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.

13 Create Your Own Tessellation Materials: 3 index cards to make 3 (3x3) squares Pencil Scissors Markers, crayons or colored pencils Poster board (larger than 8 x11 )

14

15 Translations - a slide

16 Translations - a slide

17 Reflections - mirror images Watch this video:

18 Glide Reflections

19 Rotations - turns

20 Rotations - turns

21 Seeing a Figure 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. 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.

22 Putting It All Together 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. Be sure that your whole page is filled with a repeating pattern. Color in your picture creatively. Elephants Translation symmetry Elves and Elephants Combinations of symmetry

23 Check out these websites for more information on how to make a tessellation

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