Geometric Transformations and Wallpaper Groups Introduction Lance Drager
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Wallpaper Groups Lance Drager Geometric Transformations Resources A Project to Start On Geometric Transformations and Wallpaper Groups Introduction Lance Drager Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 2010 Math Camp Wallpaper Groups Outline Lance Drager Geometric Transformations Resources A Project to Start On 1 Geometric Transformations 2 Resources 3 A Project to Start On Wallpaper Groups Lance Drager Geometric Transformations Geometric Transformations and Wallpaper Groups Resources A Project to Start On A Wallpaper Pattern Wallpaper Groups Lance Drager Rosette Patterns Geometric Transformations Resources A Project to Start On A Rosette Pattern Wallpaper Groups Lance Drager Frieze Patterns Geometric Transformations Resources A Project to Start On A Frieze Pattern Wallpaper Groups Resources Lance Drager Geometric Transformations Resources A Project to Start On • www.math.ttu.edu/~drager • Copies of Slides • Handouts of Slides • Supplementary Materials • email: lance.drager@ttu.edu • Lance Drager: (806)787-0615 Wallpaper Groups Symmetries of an Equilateral Triangle Lance Drager Geometric Transformations Resources C A Project to Start On A B Wallpaper Groups Example Symmetries 1 Lance Drager Geometric Transformations Resources • Call this one r . C A Project to Start On B r A B C A Wallpaper Groups Example Symmetries 1 Lance Drager Geometric Transformations Resources • Call this one r . C A Project to Start On B r A B C A • Call this one s. C C s A B B A Wallpaper Groups Example Symmetries 2 Lance Drager Geometric Transformations Resources A Project to Start On • Here is rs C C A s A B r B A C B Wallpaper Groups Project Lance Drager Geometric Transformations Resources A Project to Start On • Print out the triangle twice. Cut one of them out. Put the cutout down on the second sheet. How many ways can you lift it and set it down on the outline. • Name all of the symmetries and construct a multiplication table. • See if you can write all of the symmetries as products of only two of them. • Do the same for the square.
