This is a CD about teaching and learning Math/Art and geometry.
The CD does not contain artistic creations from Dutch artist M. C. Escher.
People interested in Escher art should purchase products licensed by Escher
The CD contains explanation of Escher art and some illustrations in passing.
Although there are many high resolution images of tessellations, the Escher
in low resolution to avoid copyright problems. All commercial
use of images should
seek copyright release from the creator of the image.
Tessellations is a good entrance to teach geometry and it is also a broad
Here is a screen shot of the "Table of Contents" to show the scope of the CD.
The Dutch artist M.C. Escher is famous for the animal forms that fit together
He is interested in the broad topic of space and geometry.
Tiling with geometric patterns is around for several thousand years.
It seems Escher has ignated an interest in people across different cultures.
The following screen shot shows a portion of people following
Escher's ideas and inspiration.
Knowledge of MATH is not necessary to make beautiful tessellations. I found that people with
art talents do the best. Many craftsmen made besutiful designs. In the CD, I showed how people
from all different backgrounds approach this topics. This biographic approach is facinating to me.
Mr. M.C. Escher remains a unique and most admired person in this field. Many
people hope to
have the same talent and influence. I found his ideas are
used in many differnt situations.
This can be tricky business because
Escher art is copyright protected. There may be
loyalty involved when
using Escher name or images. It is much better to develop your own ideas
for people interested in commercial products.
This is why the CD is created as a teaching tool.
I first heard about "Fractal Tiling" from Dr. Robert Fathauer. As I learn more
about this topic,
it seems fractal ideas are closely related to "Space" and "Division". The Lego and the Pineapple
are my original contribution to
the WWW. The photo of the Pineapple was taken by my friend
Dr. Ron Hurov. This is still a new field and a lot is discovered every year.
David Chow made this Twin Dragon animated GIF when he was in 10th grade. Computer graphics
is fun to learn for school children. The ideas in this
animation is original and not found
anywhere else. David Chow entered
college in Tucson Arizon in August 2006. He is paying
for his education
doing webpages and working Internet related part-time jobs.
The CD contains
many more animated GIF made by David Chow and other
less famous people. It is my hope that
all school children will be shown
the tools and the magic of computer graphics.
Examples of quilts using tessellations ideas.
There are many architecture tiles all around the world. Escher himself learn the basics of
tessellations from the Islamic tiles in Alhambra, Spain. This CD contains over 300 examples of
tessellations in craft and architecture. Once a good design is made, it will be there for thousands of
years for other people to learn and to think. I hope everyone will see and maybe go to
the original location to pay respect.
Lattice windows are used in Chinese gardens as a porous divider. These windows
to pass freely and also provide some degree of security and shading. I found similar and
more elaborate design with Jali screens.
In USA, we have concrete blocks with large openings.
There are also
metal screens with interesting hole patterns. This is an area for improving
design. As I travel, I collect images about things people do in
The Pysanka in Vegreville was design and built by Professor Ron Resch. It was
on a computer. It is huge and imposing and it is beautiful.
This is one of the best example of
3-dimensional tessellations. This CD
contains an extensive discussion of the design and
construction of this egg. The CD also contains a very large collections of photos
to this sculpture.
Tessellations do not end in 3 dimensions. There are tiling problems and
solutions in the 4th
dimension. The CD shows some examples of tessellations in 3 dimensional space. Origami
tessellations is an established topic with applications in foldable furniture and
solar collectors. This is a bit pass high school level. However, the Escher spheres and
tessellated polyhedrons are popular and well known.
If you are interested in teaching or learning tessellations, please take a look at this CD:
Buy this CD from Tessellations.com
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