On the next page, we'll see tiles that DO flip over. The cats and the ducks are also "tiles" that translate/slide/glide left or right, up or down, to fill in the picture. Now take a look at the other pictures on this page. The original line XY is "translated" along the Y axis to make line X 1Y 1. The finest examples of tessellation patterns in architecture and art can be found in Islam. If you want a larger tessellation, choose larger. In math class, we'd say that we can move a line along a graph by saying "X=Y" for the original line and "X 1 + 4 = Y 1" for the line that would be 4 boxes above it on a piece of graph paper. The piece of paper should correspond to the volume of your tessellation. So, why do we call it "translation"? Well, we call that movement a "translation" because we "translate" the tile along the X-axis and the Y-axis. This kind of tessellation symmetry- tile repeating- is called Translation and/or Sliding. The tiles in this picture are copies of one another that are simply shifted from one place to another, without tilting or flipping them over or resizing them. The tessellation is made by repeating the tile over and over again, and fitting all the copies of the tile together. This is the basic "tile" shape of the first tessellation on this page.
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