Cordon Art has the rights to Escher's work. They have graciously
allowed me to use images of his work.
All M.C. Escher works (c) 2001 Cordon Art - Baarn - the
Netherlands. All rights reserved. Used by permission.
Here are some examples of topics we discuss in class:
We explore tesselations (sometimes called tilings) as shown in the following examples. The natural question is "How did he do it?"
We look at the art which inspired M.C. Escher, and we discuss the techniques Escher used to create these wonderful images. One of the projects in the class is to make your own tessellation. Further down on the page are links to student work. Students are of course NOT graded on their artistic ability! We are looking for the ability to incorporate what was learned into a practical application.
Escher also decorated spheres like
the one shown on the left. What mathematics do we need to understand
this type of art work? We found that the tessellations on a sheet of
paper were based on geometric shapes like squares and triangles. What
kind of geometric shapes can you put on a sphere? The answers will
surprise and amaze you! You will discover what is called "Spherical
geometry" in the process of answering these questions.
This leads to the question: What other geometries are there? There are actually many more. One is illustrated in the tessellation of this disc:
We will discuss some intrigueing prints like the Mobius band below. If you trace the ants around the band, you will notice that the band has only one side! This is strange. Most objects we think about have two sides.
Escher played with some of the techniques in art. The drawing on the left plays with your sense of perspective. The print on the right is based on Penrose's impossible triangle (the figure in the middle). Using these impossible geometric constructions allowed Escher to create these types of illusions where water seems to be flowing up!
There are more topics than the ones mentioned above, but this gives you some idea of the course.
The syllabus for this course can be found here.
This course was first offered in the Fall of 2000. One of the projects was to create your own tessellation. Students came up with a variety of tessellations. Some of the examples can be found here: John Stroup, Laurie Mayuiers, Kirk Hinkelman, John Scalzo, Rachel Beatty, Cliff Holzhauser, Sabrina Lohr, Scott Nauert
If you are interested in Escher's art, then you should knnow that the official website is www.mcescher.com
Examples of Escher's tessellations can be found at many places on the Web, but "Neal's Escher Page" has a lot of examples.
Here are some shortcuts to more examples of tessellations, impossible figures, more impossible figures, hyperbolic geometry
www.mcescher.com The official M.C. Escher Webpage
The brochure for this class.
Mathematical Classification of Tessellations This page is part of a webpage which was created as an educational tool as part of a contest.
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Anneke Bart's webpage
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