Transcript Creating Your Own Tessellations

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
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.”
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
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.
Tessellations by M.C. Escher
Famous Tessellations
• This is one of
Escher’s most
famous tessellations.
It is simply called
“Reptiles”
Bulldog
(Tessellation 97)
Pegasus
(Tessellation 105)
Lizard
(Tessellation 104)
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.
Transformations
• Geometric shapes
Translation
Reflection
Rotation
Glide
Reflection
can be translated,
reflected, rotated,
or glide reflected.
• These movements
of the shapes
create a more
interesting
tessellation design.
•
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.
Create Your Own
Tessellation
Materials:
• 3 index cards to make 3 (3x3) squares
• Pencil
• Scissors
• Markers, crayons or colored pencils
• Poster board
• Piece of construction paper
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 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.
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
Check out these websites for more
information on how to make a
tessellation…
http://www.youtube.com/watch?v=ynHQU9rFlhg
http://teacherweb.com/MD/CentennialHS/MrStephenLee/Tessellations---Glide-Reflections.pdf
http://www.youtube.com/watch?v=Lc4LGZwlcvs
http://www.tessellations.org/tess-symmetry2.shtml
So, as you can see, tessellations are
fun to learn about and easier to make
than perhaps, you originally thought.

Enjoy making
your own
tessellations!