Written theory

In the videos it was explained what rotational and point symmetry was, what the difference between, line, point and rotational symmetry is and even the order of rotational symmetry. Which is basically: how many times can I rotate the figure or image to look the same.
Now let’s look at the image below.

Here we see 3 figures. And all three have rotational symmetry.
Now the first one has an order of 2, the second one an order of 3 and the third one an order of 5.
In math we not only want to know the order of rotational symmetry but also the smallest possible angle of rotation a figure has.

For this we use the order of rotation and the fact that a figure rotates 360 degrees to come full circle (become itself again).
The way we calculate the smallest angle of rotation is we divide 360 by the order of rotation.  

Now let’s calculate the smallest angle of rotation for the three figures:

  1. 360 : 2 =180 degrees. Oh, but wait if a figure’s smallest angle of rotation is 180 then it was also point symmetrical. So, this one has both point and rotational symmetry.
  2. 360 : 3 = 120 degrees.
  3. 360 : 5 = 72 degrees.


Now remember if a figure has 360 degrees as the smallest angle of rotation the figure does not have rotational symmetry!