We have an A4 sheet of paper and some scissors available: it is possible cut out the sheet in order to be able to pass through it? We can bend and cut it as much as we want, but we can’t reattach it to form a ring.
At first instinct, what you would probably do is fold the sheet in four and cut along the edges so as to obtain a hole that runs through the entire sheet, leaving it only with the edge, i.e. the perimeter. This way, however, you get a hole that is too small!
So what is the solution? The trick to use is to be able to cut the sheet in such a way as to exploit its entire surface! In this way we will obtain an edge that will not be as long as the perimeter alone, i.e. the sum of the sides, but which will be almost as long as its area, i.e. the multiplication of the sides, much larger!
To do that, what we need to do is fold the sheet in halfand then practice gods parallel cuts to the shorter side, alternating the starting point from one long side to the other, as in the image below. Once this process is finished, they go cut the ends of the sheet along the long side for all the folds we find, except the two lateral ends.
At this point, they pull the edges of the paper, we will see a very large figure appear, which will have an edge long enough to pass through! This simple game shows us the difference between perimeter and area of any geometric figure, especially in the case of convex polygons as in the case of a rectangle like our sheet.
