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Order of Rotational Symmetry

Discussion in 'Mathematics' started by Mac the Maths, Oct 30, 2003.

  1. "How many times does it fit into itself?"

    This is equivalent to set definitions and hold true for all dimensions.

    Hence F has order 1, not 0. Many texts have this wrong (IMHO).
     
  2. The points of view on this thread just keep going round and around, don't they?
     
  3. For the cognoscenti:
    exp(i*0)= 1 = exp(i*2pi)
    So one, nought (none) and a complete rotation are rather closely related.
     
  4. Frustum - when would you use rotational symmetry in real life?
     
  5. The problem here is that 'no symmetry' is interpreted as 'order 0' which us untrue. Why don't we say that 'order' of rotational symmetry is merely a label, and 'no symmetry' is a description.

    Thiis way, 'no symmetry' and 'order 1' can co-exist as the same thing.
     
  6. I have just taught a lesson on rotational symmetry which reminded me of this thread.

    This may not be a new idea but I had a great lesson using MS Word and a digital projector. With the Drawing toolbar on I created several shapes; square, rectangle, triangles, etc. Then select a shape and choose 'Free rotate' from the draw menu and use the mouse to rotate the shape and investigate rotational symmetry.

    Having done this I have realised that I can use the 'Flip horizontal' & 'Flip vertical' options to investigate reflection symmetry too.

    I now plan to create a Word Template that the pupils can use themselves in the IT suite.
     
  7. whelk

    whelk New commenter

    I think you could argue that it it is part of tessellating - eg tiling.

    There are lots of real world objects that need it - eg propellers.

    I took of photo of a lorry I was following the other day. One set of wheels was off the ground because its load had shifted.

    I covered an art class at the end of last term that was using the idea too.
     
  8. frustum

    frustum Star commenter

    Sorry - missed the question above.

    Unfortunately right now I can't think of any really _practical_ uses, but there's all the appreciation of shapes and design - habcaps, logos. Oh, and the cut of my favourite series of jigsaws has rotational symmetry - sometimes I find an edge piece fits the space but not the pattern - so I try it in the corresponding space.

    Something that's struck me since:
    You know how if you show children a parallelogram, lots of them are convinced that it has a line of symmetry? Well, I think that's because they can instinctively see that there is some repetition to it - but they haven't yet mastered (or met) the concept of rotational symmetry, so they assume it's what they do know about - reflection symmetry.
    In a way, teaching them about rotational symmetry is answering the question "Why does it make me think it's symmetrical, even though I've just folded it along every possible line and can see it isn't?"

    I've just thought of another practical one - laying a table. Admittedly, I guess many children master the concept without the language on this one, thus contradicting my earlier statement. (Actually, I doubt whether tables get laid in the homes of most of my pupils.)
     
  9. frustum

    frustum Star commenter

    That should have been hubcaps, not habcaps!
     
  10. Just wondering what the oldest topic/post on this forum was....
     
  11. Any number to the power of 0 has the value 1. ergo F has rotational symmetry order 1.
    Easy and obvious.
     
  12. This is no longer the last post in this forum
     
  13. DM

    DM New commenter

    Can we move the first sentence of post 31 to the Correcting Colleagues thread?
     
  14. I'm copying and pasting as I type
     
  15. I suspect that most would agree but the problem is finding out what the word appropriately means! Also in my experience the current approach puts such a fear and loathing of maths into many pupils that it effectively rules out them ever becoming late bloomers.
     
  16. DeborahCarol

    DeborahCarol New commenter

    It's good, Jonny - thank you! Seems you go with the '1' brigade. I do too.
     
  17. Guish

    Guish New commenter

    Good stuff. I'm sharing the link with the students. Keep it up.
     

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