Åk 6–9

4.1 Symmetry
Symmetry in mathematics is a consistent pattern. A common notion of symmetry is that if an object can be divided into two equal parts, then it is symmetrical. The definition is correct but it is not the only type of symmetry.

In order todescribe symmetry, we can say that symmetry contains an identical form repeated in a certain manner. We will look here at two types of symmetry:

- Mirror symmetry
- Rotation symmetry

Mirror Symmetry 

Mirror symmetry is the form of symmetry we common describe when we define the concept of symmetry. If an object can be divided into two equal parts by a line, then we have a mirror symmetry. This line is called the line of symmetry.

Rotation Symmetry

If a figure is rotated around a point, when it reaches an entire rotation (360o), it will look exactly the same as it did from the beginning. If during some time during this rotation, before we reach an entire rotation, see the figure completely cover its original value, then we have a rotation symmetry.

The number of times the same figure appears during the rotations determines the figure’s rotation order.

Rotation order 2
Rotation order 5

This can be calculated by:


= Rotation order

n is the number of degrees the figure must be rotated before we get the exact same figure again.

The letter Z must be rotated 180o before we get the exact same figure again. In other words, n = 180.


= Rotation order 2

An object can have more than one type of symmetry. The star in the picture has both a mirror symmetry and a rotation symmetry. The rotation order is 5.