Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations?
I think my chemistry teacher have show me once how to make it during the chem lab class, but I forgot how to do it.
The simplest way will be chose as best answer!
If the paper is infinitely thin, transparent and of size $A_n$, fold the it in half twice to get an $A_{n-2}$ rectangle. From the corner that was the middle of the piece of paper, fold diagonally to get a trapezium, then fold diagonally again infinitely many times. With the remaining infinitesimal wedge of paper, make a pencil mark about half way along one side of the wedge, then turn it over and trace over the pencil mark, then unfold once and connect the two pencil marks using the straightedge and cut along this line. Unfold the circle.