TESSELLATIONS
Presentation By Allison Cornish
ECA551 Primary Art Education Assignment One. Student No. 201147675
WHAT IS A
TESSELLATION?
Tessellations are repeating
patterns of distinct shapes.
A tessellation must follow three
rules:
This is a true tessellation. It
fits all of the 3 rules.
•The pattern must be repeated
•There must be no gaps or
overlaps
•The pattern must be able to
continue on a plane forever
This is a not a tessellation but
a pattern.
The Images on this page are borrowed from http://library.thinkquest.org/16661/cgi-bin/printpage.cgi
WHICH SHAPES
TESSELLATE EASILY?
Look at these shapes.
Which ones do you think will fit together to make a
repeating pattern with no gaps?
on each shape to find out if they tessellate.
CLICK HERE WHEN YOU HAVE FINISHED WITH THE SHAPES
Squares
YES !!!
A Square Shape
tessellates really well.
What does the first
pattern remind you of?
Notice that the square
pattern doesn’t have to
line up to tessellate?
GO BACK
Triangles
YES !!!
Triangles can tessellate too.
Are all the triangles facing
the same way?
Why do you think this is?
What would happen if they
were?
Would the shape still
tessellate?
GO BACK
Circles
NO !!!
Circles don’t tessellate.
Why is this?
Which rules of tessellation
does this pattern break?
GO BACK
Other Shapes
YES !!
All of these shapes
tessellate.
GO BACK
Octagon, Pentagon
YES !
Notice the octagon leaves gaps
in it’s pattern - so it breaks one of
the rules of tessellations - but
each gap is exactly the same - a
diamond. Sometimes two shapes
can be joined together to make a
tessellating shape.
NO ! The Pentagon
doesn’t fit
together at
all!
GO BACK
TECHNIQUES USED TO
TESSELLATE
ROTATION
R
TRANSLATION
Angle = 90º
R
R
R
Center
To rotate an object means to turn
it around, Every rotation has a
center and an angle.
To Translate an object means to
move it without rotating it. Every
translation has a direction and a
distance.
Images on this page were adapted from images at http://library.thinkquest.org/16661/index2.html
TECHNIQUES USED TO
TESSELLATE
REFLECTION
GLIDE -REFLECTION
To Reflect an object means to
produce it’s mirror image.
Every reflection has a mirror
line.
A Glide reflection combines
a reflection along with a
translation along the
direction of the mirror line.
Images on this page were adapted from images at http://library.thinkquest.org/16661/index2.html
ACTIVITY
On a piece of paper, draw an example of the four
techniques we can use to make a tessellating
pattern.
ROTATION
TRANSLATION
REFLECTION
GLIDE REFLECTION
It might help to use a mirror to check your reflection work !!!
HISTORY
Tessellations have been around a long time. In 4000
B.C. the Sumerians used them to decorate the walls
of their homes and temples . Have a think about what
the tessellations may have been constructed from so
long ago.
Can you guess?
They were made from slabs of hardened clay.
Throughout history the Egyptians, Moors, Romans,
Persians, Greek, Byzantine, Arabic, Japanese, and
Chinese have also used tessellations for decoration
and in their Art works.
Tessellating Art works from these cultures tell us a lot
about the lifestyle and culture at the time they were
made. For example, the Islamic religion forbids the
representation of living objects in works of art.
Islamic art works such as the Jam’aa Mosque
opposite, use tessellating patterns but never depict
human or animal shapes. Notice the diamond shape
pattern in the bottom center of this picture.
Image borrowed from http://islamicart.com/pages/architecture/decor.htm
WHO WAS M.C. ESCHER?
Escher is one of the best known Artists to use tessellations in his work, but was
he more than an Artist? He was considered a great mathematician too.
Maurits Cornelis Escher was born in the Netherlands in 1898. He didn’t do well in
most subjects at school and failed his final exams, however Escher did excel in
one subject, drawing. His Art teacher taught him how to make linoleum prints and
this was the beginning of his great career as an Artist. Later Escher studied
Graphic Art and created many incredible works of art. He is most famous for his
‘impossible drawings’ and his tessellations.
Escher discovered the tessellating
patterns of Moorish Mosaics during a
visit to Spain in 1922.
A great deal of Escher’s tessellations
and geometric works were developed
using mathematical techniques.
Impossible?
Images on this page were found on the Web. See Acknowledgements Page.
ESCHER’S
TESSELLATIONS
Escher uses REFLECTION and
ROTATION to create this art
work.
Can you tell which technique
was used first?
All Images on this page are borrowed from http://library.thinkquest.org/16661/index2.html
ESCHERS
TESSELLATION’S
Which technique has Escher
used to create this tessellation?
All Images on this page are borrowed from http://library.thinkquest.org/16661/index2.html
ESCHERS
TESSELLATION’S
Escher has created a new shape staring from a Square. Notice how the top and
right-hand-side lines are the same? So are the bottom and left-hand-side lines.
This allows the shape to fit together. What would happen if we tried to use
different lines to create a new shape? Would they fit together? Try it on graph
paper first and then copy the technique Escher has used.
All Images on this page are borrowed from http://library.thinkquest.org/16661/index2.html
ESCHER’S
TESSELLATION’S
Notice how Escher has used
the ROTATION technique in
this Art work.
Find the center point. This is
the point the shape must
rotate around.
All Images on this page are borrowed from http://library.thinkquest.org/16661/index2.html
ACTIVITIES
Make your own tessellating shape
from a square.
First Cut out a section from the bottom
and stickytape it to the top.
Do the same for the sides.
Cut out different color copies of your
shape and stick them to cardboard to
form a tessellation.
USEFUL WEB SITES
TOTALLY TESSELLATED
http://www.thinkquest.org/library/lib/site_sum_outside.html?tname=16661&url=16661
TESSELLATIONS WEB QUEST
http://www.angelfire.com/ab6/rbrowning/
WHAT ARE TESSELLATIONS
http://www.tssp.co.uk/Literature/Tessellations/WhatareTessellations/
ISLAMIC ART
http://www.islamicart.com/main/architecture/decorate.html
MORE INFORMATION ON TECHNIQUES DISCUSSED IN THIS PRESENTATION
http://www.ucs.mun.ca/~mathed/Geometry/Transformations/frieze.html and
http://mathforum.org/sum95/suzanne/symsusan.html
A HUGE NUMBER OF LINKS ACTIVITIES AND WEB SITE EVALUATIONS CAN BE
FOUND AT:
http://ccins.camosun.bc.ca/~jbritton/jbsymteslk.htm
ACKNOWLEDGEMENTS
A large amount of the information for this presentation was adapted for Primary School Students from the web site
“Totally Tessellated” (http://library.thinkquest.org/16661). I would recommend this site to any teacher planning to
introduce tessellations to their students.
Picture and Video Images
base of the Friday Mosque "Jam'aa" at Herat in Afghanistan from:
Islamic Arts and Architecture Organization, 1995-2001.,‘Islamic Ar t’,
<http://islamicart.com/pages/archtcre/décor.htm> (last accessed 24/4/02)
All other Picture and Video images from
Bhushan, Kay and Williams, n.d. ‘Totally Tessellated’ <http://library.thinkquest.org/16661> (last accessed 24/4/02)