According to various web publications, folding a single sheet of paper several dozen times would result in a thickness approximately equal to the Earth-Moon distance. This is possible in theory, but in reality, we would obviously be unable to achieve it.
In a publication, the Maths en Direct platform explains an amazing theory. Let's take a simple sheet of classic A4 paper, the thickness of which is 0.1 mm. By folding the latter 42 times in a row , it would be possible to obtain a thickness exceeding the Earth-Moon distance. Remember that the distance separating our planet from its satellite is 384,400 kilometers . This is obviously an average distance, because in reality it constantly oscillates between 356,700 and 406,300 km.
Note in passing that this is indeed the lunar distance , not to be confused with the astronomical unit (AU). The latter corresponds approximately to the distance between the Earth and the Sun, approximately 150 million kilometers.
First of all, let's remember that with each folding, we double the number of thicknesses . At the end of the third folding, the thickness of the sheet is equal to 0.1 × 2 × 2 × 2 =0.1 × 23 =0.1 × 8 =0.8 mm. Following this logic, we get 0.1 × 242 =439804651110.4 mm after 42 bends. In a Quora post, an engineer presents the calculation differently:2^42 (2 to the power of 42) thicknesses of paper, or 4,398,046,511,104 thicknesses, or 4.4 trillion (or 4,398 billion) thicknesses. Multiplying by a thickness of 0.1 mm we get 439804651.1104 m and therefore more than 439,804 km.
While this theory is completely valid, putting it into practice remains completely impossible. Indeed, the surface obtained would be infinitely reduced. In addition, another much simpler reason explains this impossibility:it is usually very difficult to fold an A4 sheet more than 8 times . Despite the infeasibility of the thing, this kind of reasoning remains interesting. On the Secouchermoinsbete platform forum, user Touko wrote:
"It's true that this type of reasoning is infinite:if I crush a Carambar, it goes to Saturn and if I unfold the atoms of a seed of couscous, I go around the earth a million times… we don't get by anymore! »
Here is an explanatory video published by TED-Ed in 2021:
