# Rotational Symmetry

Discussion in 'Mathematics' started by FlippantFlyer, May 11, 2011.

1. ### FlippantFlyer

Exactly the reason why using zero order of rotation may be reasonable. Although I accept it is universal practice (now) to use min of one order of rotation.
Whatch out for the grammar police!

2. ### NazardNew commenter

Thanks for your posts, Kevin - it is really helpful to have an insight to the workings of an awarding body.
This is an interesting definition. I had always previously felt safe making statements such as: "the rotational symmetry of a rectangle is order 2", when actually under your definition it might not be.

3. ### Betamale

Polygons or patterns?

4. ### kevchenko13

Thanks for the replies
Yes, and if we ask for the order of rotation symmetry we accept 0 as an alternative to 1 (but not 1 as an alternative to 2, etc).
I can cite precedent! The 1999 National Curriculum, statement Ma3.3(b).
I don't follow why it might not be. A rotation of 360 / 1 would work, so would 360 / 2 and then I don't believe there are any larger integers that do, so the order is 2.
I probably should have given the specification statement as well as the definition:
<font size="3" face="ArialMT">"Recognise and visualise the rotation symmetry of 2-D shapes. Identify the order of rotation symmetry. Complete shapes and patterns to give a specified order of rotation symmetry."
</font>Polygons and axes of rotation don't feature in the spec. I think (hope) that the definition can be taken to extend to 2-D patterns as well!
Thanks again
Kevin

5. ### NazardNew commenter

Unless your rectangle happens to have all its sides the same length in which case the order ceases to be 2 but all of a sudden becomes 4...

6. ### kevchenko13

Ah, now I'm with you. So what's the order for a parallelogram then?

7. ### NazardNew commenter

It might be 2. It might be 4.
To be fair, I suppose there is a similar issue with "how many lines of reflection symmetry does a parallelogram have?" - it might be 0 or 2 or 4.
I don't have a particular issue with the detail of rotational symmetry, but saying that a shape "doesn't have rotational sym" doesn't quite feel the same as "order zero".

8. ### kevchenko13

Yes, the issues often come from how we define our quadrilaterals. Venn diagrams are not included in the single GCSE but you might introduce the idea that squares are also rectangles and rhombuses, rectangles and rhombuses are also parallelograms and that the argument doesn't always flow back in the other direction.
Do you feel differently about the phrases 'doesn't have reflection symmetry' and 'zero lines of reflection symmetry'? Why?