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The Penrose Tile Title

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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.


My high school students at Campbell Hall have created this project to practice their newly acquired animation skills using Macromedia’s Director. The topic I chose had the potential of appealing to students’ interests by working on a game-like phenomenon, such as a Kaleidoscope, with the chance of drawing their interest to the underlying concepts that they were reluctant to engage in otherwise. 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. Computer education in those days focused on delivering computer skills without tying them to the topics that can benefit from using them. This is probably changing as we speak and generally speaking schools are much more aware of the important role that technology is assuming in every aspect of our life.


In a contemporary class, this type of project would have been initiated by the Math teacher and supported by the technology team of the school. As such, it would have had a prominent effect on the depth and breadth of the project and subsequently increase students’ learning experience. I envision a project that deals with ‘The Math of Penrose Tiles’, ‘Tessellations and Tiling’, ‘Non-periodic Tiling’, ‘The Chemistry of Crystals’, ‘Barlow’s Law’, and more. All linked together in a hypermedia scheme designed to present the various perspectives that are part of this subject. In order to enhance the project even more, I would assign different aspects of it to different groups of students and have them collaborate on putting it all together in a cohesive final presentation.

The Penrose Tiles Project

Click here to see the Penrose Tiles Project


Click to see a student version of the Kaleidoscope



The Penrose Tiles The Virtual Gallery The Castle of Time Where in the World The Mission Home
Introduction Discovery and Constructionist Learning Home The Mission Where in the World The Castle of Time The Virtual Gallery Apollo's Vision

© 2006, Miriam Bogler Friday, April 7, 2006

Introduction Discovery and Constructionist Learning Home The Mission Where in the World The Castle of Time The Virtual Gallery Apollo's Vision