What fractions can you find between the square roots of 65 and 67?
Weekly Problem 4 - 2012
What fraction of the volume of this can is filled with lemonade?
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?
To iterate means to repeat, so an iterative process involves
repeating something many times.
Imagine some dough, Plasticine or Blu-Tack, something that can
be made into a strip then stretched.
We are going to take a length of this material, which we'll
regard as the unit length, and put a mark at some fraction distance
Now we are going to follow a procedure and see where our mark
The material is folded in the middle so that the bottom reaches
back to the top.
The material is now only half a unit in length and twice as fat,
so it is rolled out or stretched uniformly to become one unit in
Finally we'll note the new position of our mark.
What happens for other start fractions?
Does everything go to a loop?
What size loops appear and for what fractions?