Symmetry in Carpets
Azerbaijan is known for its long history of carpet weaving, which dates back as far as the second millennium BC. The traditions have evolved over time, with more complicated weaving techniques and designs, most of which employ various types of symmetry. Let's explore the various types of symmetry:
Rotational Symmetry
We'll focus on the first rug for now. The first image here is of that same rug. But the second one is a version that has been rotated 180 degrees. Notice that when we rotate the rug 180 degrees, the pattern stays exactly the same! This type of symmetry is called rotational symmetry.
Reflection Symmetry / Mirror Symmetry
Next, let's focus on the second rug. The first image here is of that same rug. But the second one has been flipped horizontally. Notice that when we flip the rug horizontally, the pattern stays exactly the same! This type of symmetry is called reflection symmetry or mirror symmetry.
We can also have a vertical reflection. Here we have the third rug normally and flipped vertically. Notice that it almost looks like this rug is symmetric when flipped vertically; however, the colors of the central flower are switched after the flip! So this rug does not have vertical mirror symmetry, unless we choose to ignore the colors. Here the pattern is symmetric, but the colors are not.
Sample Problems
1. Which of the four rugs exhibit rotational symmetry? Is the answer different if we focus only on patterns and ignore colors?
2. Which of the four rugs exhibit horizontal mirror symmetry? Is the answer different if we focus only on patterns and ignore colors?
3. Which of the four rugs exhibit vertical mirror symmetry? Is the answer different if we focus only on patterns and ignore colors?
