What fractions can you find between the square roots of 56 and 58?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
What fraction of the volume of this can is filled with lemonade?
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?