Symmetry

Mathematics is not just big numbers, weird names and mysterious people who come up with more and more confusing formulas. There are math problems that everyone understands naturally and intuitively. We all see them and recognize them right away.

What is symmetry? By asking such a question we would rather not get in the answer the correct mathematical definition. But everyone will be able to give examples of symmetrical objects in the nature. We will probably hear snowflake, human face, human body or butterfly.

So what does it mean that something is symmetrical?

In simple words, an object is symmetrical performing certain operations such as rotation do not change its shape and position. Let's take a circle, for example, we can rotate it around the center and it will be the same circle, circle has infinite number of symmetry.

However, the square is no longer so easy (:
Only rotations by 90, 180, 270 and 360=0 degrees does not change the position of the square. 360 degree rotation is unique because after such transformation the square remains unchanged. Transformation which does not change anything is called Identity. Such transformations in mathematics are called symmetries. Because the square has only four symmetries, we can say that the circle is more symmetric than the square. It is also worth noting that the rotation by an angle greater than 360 degrees is the same as the rotation by an angle from 0 to 360 degrees, for example, a rotation of 540 degrees is the same as a rotation of 180 degrees.

Symmetry is not just geometry

I want to mention that the concept of symmetry also applies to non-geometric objects. For example, palindromes -that is sequence of characters which reads the same backward as forward - Was it a cat I saw or Rats live on no evil star or in Latin Sum summus mus which means I am the mightiest mouse. Also matrices can be symmetric.