Peg Rotation

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Here we have a kind of peg board. The holes go all the way through so the pegs may be seen from the top or underneath.

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Peg Rotation


You'll see the 4 blue pegs.

Now the peg board is either:

  • flipped over - north to south, OR east to west, OR north-east to south-west, OR north-west to south-east;
  • or it is rotated clockwise or anticlockwise.


Can you find out which movements could produce the four next views?

 
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Peg Rotation
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Peg Rotation
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Peg Rotation
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Peg Rotation


You could make some of your own and get your friends to see if they can find how you've moved it to make your next picture.
Try now to put 4 pegs in so that when you do a move with the board it still looks the same.


Now I've made a triangular board to do the same things.
Here's the starting view:

 
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Peg Rotation


How has it been moved to show these views?
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Peg Rotation
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Peg Rotation


Hope you've had fun exploring these.
Can you think up ways of changing what I've done so that you can explore further?