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.
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. |