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'Dotty Circle' printed from http://nrich.maths.org/
Watch the film below.
Full Screen Version
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Try to describe what happens in the film to someone else.
Imagine the dot starts at the point (1,0), turns through $20^\circ$
and then stops:
If the point now carries on, through how many degrees must it turn
to finish the same height above or below the horizontal axis as it
was when it had gone through $20^\circ$?
Can you find a general rule for explaining when the dot will be
this same distance from the horizontal axis?
You might like to try
Round and Round and Round
after this problem.
This film is based on one
developed by Alf Coles - thank you to Alf for allowing us to use
these ideas. You can watch all Alf's films at http://www.mathsfilms.co.uk