hope college > academic departments > math > Elliot Tanis 

Maurits C. Escher  a Dutch Graphics ArtistDuring my tenure at Hope College, several students worked with me studying the tessellations of M. C. Escher. We wrote computer programs to replicate several of his tessellations as well as other work that had mathematical properties. Computer programs were written in BASIC, Pascal, and more recently we have used MAPLE. Two PowerPoint presentations have been added as zipped folders. One of these incorporates output from MAPLE. They are available at the end of this page in an unzipped format so may take some time to load. Maple worksheets that construct examples of the 17 plane symmetry groups are available in a zipped folder. First extract the files into a folder of your choosing. If you open MAPLE and then, from MAPLE, open Menu, you will be able to run these programs. Several of them contain animations. Click on the figure and then use the animation controls on the toolbar. Here are two PowerPoint presentations that I had prepared for Hope College colloquia. The first is 138 slides and incorporates IBMPC output and Tektronix 4051 output. (Escher) This word document gives a summary of the talk. (abstract) Here is a 200 slide PowerPoint presentation that incorporates Maple output. (Longer Escher) In addition to Escher related projects, other graphics projects were done, often with students. Some of those materials are now given. One creative student was Lee Kuivinen. He first started doing graphics using parametric equations. He developed some interesting designs. Examples. While searching the literature, Lee ran across an article on Circular Coordinates. He combined what he learned in that article with the work he had done using parametric equations and we published "Circular Coordinates and Computer Drawn Designs" in the May, 1979 issue of Mathematics Magazine. The paper "Tessellations and the Tektronix 4051" was presented at the National Educational Computing Conference in 1979. In March, 1981, a colloquium was presented at Western Michigan University in the College Colloquium Series. The title was "The Computer as an Interface Between Mathematics and Art" and included graphic works of M. C. Escher. After having given a talk at Central College, Pella, Iowa, as article appeared in the Central College bulletin, March, 1981, titled "Elliot Tanis Uses Computer to Simulate Art." Also, in 1981, the Holland Sentinel printed the article "Is this really art on a computer? " The Tektonix 4051 computer with a plotter were also used to write a paper that was presented at the Third World Conference on Computer Education in Lausanne, Switzerland in 1981. The title of this paper is "The Compter as an Interface Between Mathematics and Art." Another student, Bill Terkeurst, was intrigued by some of M. C. Escher's other works and wrote a paper "Relativity in Perspectivity" that was published in the Pi Mu Epsilon Journal in 1982. The Apple II computer with graphics capabilities gave us further opportunities to explore the tessellations that were created by M. C. Escher. Some of these results were presented at the Sixth International Conference on Computer and the Humanities at North Carolina State Universithy in 1983. The title of that paper is "M. C. Escher and Computers."

