KaleidoMania! applies transformational geometry to create visually attractive and interactive screenviews.
Exploring The Software:
Begin by going to the Investigations menu and opening "Instructions". You will want to practice manipulating the fundamental region in the source box.
- Change symmetries using the Symmetries button and matrix.
- Under the Pattern menu, explore "Show Grid" and "Show Fund Rgn".
- Under the Investigations menu, check out "The Tours", the "Symmetry Explorations", the Cyclic and Dihedral "Experiments", the "Isometry Puzzle" and the "Wallpaper Game".
- Explore the results of using the "Generate", "Slide Show" and "Full Screen" buttons.
- Use File > "New Source" and the palette of drawing tools to create some dramatic interaction with pattern generation.
Thinking About the Mathematics:
Understanding the notion of fundamental region is critical to the generation of the patterns.
- Determine which patterns have fundamental regions that are:
- triangular (regular or right)
- square, or
- How is the shape of a fundamental region related to the symmetry type?
- What is the meaning of the symbols on the edges and corners of fundamental regions as they appear in the source box?
- Based on your explorations, how would you express in words exactly what a fundamental region is or does?