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Transformations and SymmetryIntroduction

Reading time: ~10 min

Many geometric concepts, like lines and points, were “invented” by mathematicians. Symmetry, on the other hand, is everywhere around us. Almost all plants, animals, and even we humans are symmetric.

Over time, we’ve imitated nature’s symmetry in art, architecture, technology and design. Symmetric shapes and patterns just seems to look more beautiful than non-symmetric ones.

But symmetry is much more important than simply looking beautiful. It lies at the very foundations of our universe, and can even explain the most fundamental laws of physics.

While symmetry is a very intuitive concept, describing it mathematically is more difficult than you might think. First, we have to learn about transformations, which are ways to convert one geometric figure into another one. Here are a few examples:

The result of a transformation is called the image. The image of a figure A is usually denoted by A (pronounced as “A prime”).

The first example above is special, because it only moves and rotates the original star, but doesn’t change its size or shapes. Transformations with this property are called rigid transformations.