Objective: Objective: Students will…Students will…

(1) Understand the concept of and the process of (1) Understand the concept of and the process of making tessellations.making tessellations.(2) Create tessellations using: Rotation, Translation, (2) Create tessellations using: Rotation, Translation, ReflectionReflection(3) Understand the works of M. C. Escher.(3) Understand the works of M. C. Escher.(4) Use elements and principles of design: color, (4) Use elements and principles of design: color, balance, repetition and pattern.balance, repetition and pattern.(5) Use the skills they have learned to produce a (5) Use the skills they have learned to produce a UNIQUE tessellation of their ownUNIQUE tessellation of their own

Please read the entire PowerPoint before beginning.

Who is famous for Who is famous for tessellations?tessellations?• A man who is famous A man who is famous for his art work with for his art work with tessellation was Maurits tessellation was Maurits Cornelis Escher, from Cornelis Escher, from Leeuwarden, Leeuwarden, Netherlands. The Netherlands. The picture on the right is picture on the right is his self-portrait.his self-portrait.

• He said, He said, ““My work is a My work is a game, a very serious game, a very serious game.game.””

M. C. EscherM. C. Escher

• Most famous creator Most famous creator of tessellationsof tessellations

• Born in Holland in Born in Holland in 1898 (died in 1972)1898 (died in 1972)

• Originally studied Originally studied architecture before architecture before becoming interested in becoming interested in woodcuts and woodcuts and printmakingprintmaking

• Did 137 tessellations Did 137 tessellations in his lifetimein his lifetime

M. C. EscherM. C. Escher

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

Tessellations by M.C. EscherTessellations by M.C. Escher

Famous TessellationsFamous Tessellations

• This is one of This is one of EscherEscher’’s most s most famous famous tessellations. It is tessellations. It is simply called simply called ““ReptilesReptiles””

BulldogBulldog

(Tessellation 97)(Tessellation 97)

PegasusPegasus

(Tessellation 105)(Tessellation 105)

LizardLizard

(Tessellation 104)(Tessellation 104)

*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.

TransformationsTransformations

• Geometric shapes Geometric shapes can be translated, can be translated, reflected, rotated, reflected, rotated, or glide reflected.or glide reflected.

• These These movements of the movements of the shapes create a shapes create a more interesting more interesting tessellation tessellation design.design.

Translation

Rotation

Reflection

Glide Reflection

•Tessellations, or regular divisions of the Tessellations, or regular divisions of the plane, are arrangements of closed shapes plane, are arrangements of closed shapes that completely cover the plane that completely cover the plane without without overlappingoverlapping and and without leaving gapswithout leaving gaps. .

Typically, the shapes making up a tessellation are Typically, the shapes making up a tessellation are polygons or similar regular shapes (like square tiles polygons or similar regular shapes (like square tiles used on floors). Escher exploited these basic patterns used on floors). Escher exploited these basic patterns in his tessellations, applying reflections, translations, in his tessellations, applying reflections, translations, and rotations to obtain a greater variety of patterns. and rotations to obtain a greater variety of patterns. He also He also ““distorteddistorted”” these shapes to form animals, these shapes to form animals, birds, and other figures. These distortions had to obey birds, and other figures. These distortions had to obey the three, four, or six-fold symmetry of the underlying the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation. pattern in order to preserve the tessellation.

Materials:Materials:

•3 index cards to make 3 (3x3) squares3 index cards to make 3 (3x3) squares

•PencilPencil

•ScissorsScissors

•Markers, crayons or colored pencilsMarkers, crayons or colored pencils

•Poster boardPoster board

• Piece of construction paperPiece of construction paper

Create Your Own TessellationCreate Your Own Tessellation

First Make a

Template !

Translations - a slide

Translations - a slide

Reflections - mirror images

Watch this video: http://www.youtube.com/watch?v=QR0uK5PRzRQ

Glide Reflections

Rotations - turns

Rotations - turns

Seeing a FigureSeeing a Figure• Looking at your tessellation template, study Looking at your tessellation template, study

the sides and the shape to decide what sort of the sides and the shape to decide what sort of figure you might see.figure you might see.

• The person who designed this form saw an The person who designed this form saw an elephant and an elf.elephant and an elf.

• Are there any other different forms that you Are there any other different forms that you might see?might see?

• When looking for the shape be sure not to see When looking for the shape be sure not to see too much detail as it can make the art work too much detail as it can make the art work too crowded.too crowded.

Putting It All TogetherPutting It All Together• Take your Take your

tessellation template tessellation template and trace it on to a and trace it on to a piece of paper.piece of paper.

• When tracing you can When tracing you can use different types of use different types of symmetry to change symmetry to change your picture.your picture.

• Be sure that your Be sure that your whole page is filled whole page is filled with a repeating with a repeating pattern.pattern.

• Color in your picture Color in your picture creatively.creatively.

Elephants

Translation symmetry

Elves and Elephants

Combinations of symmetry

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

Enjoy making Enjoy making your own your own

tessellations!tessellations!

So, as you can see, tessellations So, as you can see, tessellations are fun to learn about and easier are fun to learn about and easier

to make than perhaps, you to make than perhaps, you

originally thought. originally thought.