At 14:03 16/06/2011 +0100, Moore, Robert wrote:
>Have I missed something here? I though Jane was correct.
>The question is 'how many time does the circumference of one circle go
>into the other?'. Circumference is 2 x pi x r
>If A is on the larger circle we need to divide larger by smaller
>circumference, 2 x pi will be on top and bottom of the division and cancel
>out - leaving the answer as 3. (done in your head!)
>Or is that too easy?
I got confused as well, but I then realised that it all depends upon how
one is defining 'a revolution'. If the point is marked only on the small
circle, and if the small circle starts at the top of the larger one (i.e.
with the mark at the 'south pole') of the small circle, then, in terms of
one way of thinking of it, after any integral number of revolutions of the
small circle, the mark on it will _still_ be pointing south - which means
that after one (or two) of 'that sort of revolution'), the mark would not
be in contact with the larger circle. Put another way, after one such
'revolution', the length of the small circle which has rolled against the
larger one will _not_ be equal to its circumference.
I still think the main problem is the lack of clarity in the wording of the
question!
Kind Regards,
John
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