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'Turning Cogs' printed from http://nrich.maths.org/
Pick two cogs in the interactivity below, place them near each other and turn one of them.
(You can turn a selected cog by using the arrow keys on your keyboard or by using the green arrows on the interactivity.)
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Now pick a different pair and do the same thing again.
What do you notice about the direction in which the cogs turn each time?
Now pick two cogs with 5 "teeth".
Mark a "tooth" on each cog by selecting it and then pressing the blue button. You may like to line up the marked teeth so that they start next to each other.
Watch what happens to the teeth that are marked as the two cogs turn.
What can you say about the way that the marked tooth of one cog fits into the gaps of the second cog?
Will this always be the case whichever two cogs you pick?