There is a geometric magic that, thanks to suns two scissors cuts on a sheet of paper, it takes us from a “eight” to a square. But how is this possible?
To reproduce the geometric experiment we need to take a piece of paper and cut out a cross with sufficiently long ends (5 cm). Once the cross is cut out, let’s go to join the opposite ends two by twojoining two upwards and two downwards thus forming an “eight” as in the figure below.
After that”let’s flatten” one of the two circles that form the figure eight and cut it along its longer side, as shown in the photo below.
We get like this two T’s attached along the vertical leg. Let’s join them together by overlapping them and we cut transversely along the vertical leg.
At this point, we will see a appear square after only two cuts and we will therefore have gone from a sheet in the shape of an “eight” to a square.
But how was it possible? Let’s see it through a diagram. We start from the cross cut out on the sheet and indicate with A (red) and B (blue) the segments that we have joined to form the “eight”. Cutting along the axis perpendicular to segment B we obtain two T’s attached to the base of the vertical leg, which coincides with segment A.
Now, cutting along the transversal to segment A and opening the leafletwe get just a square. This is because by cutting the “double” T in two along the vertical leg, two “half squares” are obtained which, once opened with respect to the corners B1 and B2 (which we remember to be attached B1 with B1 and B2 with B2), form an exactly whole square.
