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Confusion seems to be entirely generated within the exchanges. You posed the question: On 16-Jun-11 10:15:56, Gavin and Rosemary Ross wrote: > "A circle of radius 1cm rolls round the outside a circle of 3cm. > The point A is the initial point of contact of the two circles. > How many revolutions does the smaller circle make before it returns to > point A? Hence you specified "outside" and the number of "revolutions" of the smaller circle. While you did not write "circle of [radius] 3cm", any other parsing would be perverse and arbitrary. The circle "revolves" when a point on the circumference rotates 360 degrees relative to the centre. If the small circle slides round the large one with the marked point maintaining a fixed orientation, it has not revolved. The large circle has circumference 3X that of the small circle. In rolling round, whether inside or outside the large circle, the small circle revolves three times and arrives back at its start point. Starting at the top, after 1 revolution (360) the contact point is 4 o'clock and the mark points down, after 2 revolutions it's at 8 o'clock and after 3 revolutions it's back where it started. If you want word games, the following was related on the Today programme. Dalai Lama goes to buy a pizza. Pizza man: How do you want your pizza? DL: I want "one with everything". PM: Yessir. That will be 2-50. DL hands over 5, and waits ... DL: Where's my change? PM: Change must come from within. This email and any attachments are intended for the named recipient only. Its unauthorised use, distribution, disclosure, storage or copying is not permitted. If you have received it in error, please destroy all copies and notify the sender. In messages of a non-business nature, the views and opinions expressed are the author's own and do not necessarily reflect those of Cefas. Communications on Cefas’ computer systems may be monitored and/or recorded to secure the effective operation of the system and for other lawful purposes. ****************************************************** Please note that if you press the 'Reply' button your message will go only to the sender of this message. If you want to reply to the whole list, use your mailer's 'Reply-to-All' button to send your message automatically to [log in to unmask] Disclaimer: The messages sent to this list are the views of the sender and cannot be assumed to be representative of the range of views held by subscribers to the Radical Statistics Group. To find out more about Radical Statistics and its aims and activities and read current and past issues of our newsletter you are invited to visit our web site www.radstats.org.uk. *******************************************************