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The Penrose Tiles


Viewing Prerequisites:

In order to view this project you need to download the Schockwave Player. It is recommended to view the shockwave files on a PC because as it turns out the files are not presented properly on the Mac. These files were created with a very old version of Director (then Macromedia, today Adobe) for the PC, which might be the cause for the difficulties viewing it on the Mac.

Description:

The Penrose Tiles was a project created by the High School students of Campbell Hall. The inspiration for the project came to me from a fascinating book written by Theoni Pappas, called: “The Joy of Math”, which contains interesting examples of how math manifests itself in almost everything that surrounds us. One of these examples described the “Penrose Tiles”, which were invented by Roger Penrose in 1974 and consisted of two tiles called “Kite” and “Dart” and could produce an infinite number of non-periodic tiling of a plane. This project, which seemed somewhat complex mathematically, had the potential of getting students highly involved in it and thus generating openness to understand its mathematical concepts. My idea was to challenge students to research the Penrose Tiles, understand its basic characteristics and the various ways of tiling them in a plane and use this knowledge to create tiling patterns for a Kaleidoscope. The idea immediately attracted their attention and equipped with their new knowledge of Macromedia’s Director, they went on to create their project. In addition to understanding the Penrose Tiles and how to tile them, students had to write about them and any known links that exist in nature, such as: crystals that have fivefold symmetry behaving like Penrose 2-D tiles. The project you see here is a model I created to help me define my expectations for my students and visualize the outcome. The final outcome, as my students designed and created, turned out to be a pleasant surprise.

This experiment proved successful because students had to understand the shapes and attributes of Penrose Tiles before they could create, tile and animate them in a plane. In addition, students had to demonstrate a mastery of their animation skills and understanding of Macromedia Director’s authoring tools, as well as, understanding programming and Director's Lingo programming environment. However, I believe that the experiment would have been much more effective if it was done in collaboration with the Math teacher as part of the math curriculum in class.

The Penrose Tiles Project

Click Here to See the Penrose Tiles Project

Student Version of the Kaleidoscope

Click to See a Student Version of the Kaleidoscope

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