The aim of this demonstration is to cut a hole in a small piece of paper (1/4 of an A4 sheet) which is large enough to fit a person through.
An object with a small area can still have a large perimeter.
A small piece of paper (we use 1/4 of an A4 sheet) and a pair of scissors.
To start with, fold the paper in half. Next make a series of cuts in from the fold, making cuts roughly 1 cm apart, which stop roughly 0.5 cm from the edge.
Now make a series of cuts in from the other side. Make sure you cut between the first set of cuts (see diagram).
Finally, cut along the fold, but leave the two end segments intact.
If you unfold the paper, it should be two long zigzags. Pull it out and you will get a loop large enough to fit a person through.
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The pattern of cuts and the resulting hole. |
Depending on the motor skills of the people trying it, you can use larger pieces of paper.
This demonstration helps to show the difference between area and perimeter. Although the area of the paper stays the same, the perimeter changes dramatically.
According to legend, the ancient city of Carthage was founded by a group of refugees. When they asked for some land to build a home on, the locals said they could have as much land as a cows hide could encompass. Through cutting up a cows hide very finely, they were able to set aside enough land to found a city.
In modern mathematics, there are many shapes which are small in area, but have a large perimeter. Some even have an infinite perimeter. Many of these can be found in the study of Fractals.
This effect also happens for the volume and surface area of three dimensional objects. For example, your intestines fit into a volume smaller than a basketball. Because of their twisted shape and wrinkly interior, if your intestines were cut open and spread out flat they would have an area more like a basketball court. Do not try this at home.
The old lolly wrapper challenge. How long a strand can you tear a lolly wrapper into?
