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Escherization The Tilings of Escher

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... 1972) is one of the world's most famous graphic artists. During his lifetime, Escher made 448 lithographs, woodcuts and ... Dutch Graphic Artist M.C. Escher ... – PowerPoint PPT presentation

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Title: Escherization The Tilings of Escher


1
Escherization (The Tilings of Escher)
Curtis Lyons
2
Dutch Graphic Artist M.C. Escher
Maurits Cornelis Escher (1898-1972) is one of the
world's most famous graphic artists. During his
lifetime, Escher made 448 lithographs, woodcuts
and wood engravings and over 2000 drawings and
sketches. He is most famous for his work
involving tilings or tessellations.
Eschers Escher Escherized
3
  • Escher began experimenting with different
    pictures and shapes, creating pictures that would
    come to be known as tessellations.

4
The Escherization Problem
  • Given a shape S, find a new shape T such that
  • 1 T is as close as possible to S and
  • 2 Copies of T fit together to form a tiling of
    the plane.

5
  • This means that
  • Given a shape S, we can take a piece out of the
    shape and place it somewhere else on it. We have
    now formed a different shape T, that is close to
    the original.
  • This T must be such that when copied and
    transformed, perfectly fills the plane.

6
  • There are three types of transformations that may
    be applied to our figures in order to obtain a
    complete picture in the plane

Reflection/ Flip
http//garnet.acns.fsu.edu/7Ejflake/math/GeomSp/G
SFlip.html
Rotation/ Turn
http//garnet.acns.fsu.edu/7Ejflake/math/GeomSp/G
STurn.html
Translation/Slide
http//garnet.acns.fsu.edu/7Ejflake/math/GeomSp/G
SSlide.html
Many more examples of this can be found
at http//library.thinkquest.org/11750/eschpage/T
ess1B.html
7
  • Of course there are many more difficult
    applications of tessellations than are shown
    here. Some pictures of these follow

8
Homework Problem
  • This problem is to be done in GSP and turned in.
    The directions can be found at the following
    website
  • http//mathforum.org/sum95/suzanne/tess.gsp.tutori
    al.html
  • Feel free to be creative with your random
    shape!!

9
In closing...
An old Babylon proverb asks, What did the acorn
say when he got older?
Ge-om-e-try!!
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