Symmetry

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Symmetry is a characteristic of geometric figures and other abstract mathematical elements. This, when it is identified that there is correspondence with respect to a center, axis or plane.

That is, a figure shows symmetry, for example, when turning it 180º maintains the same image. Consider, for example, a four-pointed star that has each of its sides the same as the other.

There are several types of symmetry, as we will explain in the next section.

Types of asymmetry

Among the main types of symmetry, the following stand out:

  • Central symmetry: It is the situation in which homologous points are identified with respect to the point that is called the center of symmetry. In other words, each point corresponds to another located at the same distance from the point of symmetry.

In formal terms, the central symmetry can be defined from the following rule: If we have points X and X ', both are symmetric with respect to a center (C), if segment CX is of equal length as segment CX' , so that X and X 'are equidistant from C.

Let's think of two geometric figures, one being equal to the other if it were rotated 180º, and both are at the same distance from a point (the center C), as we see in the image below:

  • Axial symmetry: Axial symmetry is one that is fulfilled as a function of an axis. This, unlike central symmetry, which is relative to a point.

That is, there is axial symmetry when all the points of a figure correspond to those of another, being equidistant from the axis of symmetry. Therefore, for points A, B and C there would be their corresponding homologous points A ', B' and C '.

To explain it more graphically, let's think about the drawing of a human silhouette on a sheet of paper. Then we fold the sheet in two, dividing the image into two equal parts. In this way, we will have two figures, one that would appear to be the reflection of the other in a mirror.

  • Radial symmetry: Radial symmetry, or rotational symmetry, is the property that an object has when, when making a partial turn, its image does not change, as in the bottom drawing where a 180º rotation has been made.

This type of symmetry is fulfilled when, when drawing an imaginary line that passes through the center of the object, it is divided into two parts that, in turn, are equal.

We can specify that there exists a discrete rotational symmetry of order n, rotational symmetry of n-folds, or discrete rotational symmetry of order n, when the rotation occurs at an angle of 360 ° / n. In other words, a symmetry of order 2 is that observed when the object rotates 180º.

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