Introduction
Physics is one of the greatest and most important sciences studied by man. Its presence can be seen in all spheres of life. Not infrequently, discoveries in physics change history. Therefore, the great scientists and their discoveries, over the years, are still interesting and significant for people. Their work is relevant to this day.
Physics is the science of nature that studies the most general properties of the world around us. It studies matter (substance and fields) and the simplest and at the same time the most general forms of its movement, as well as the fundamental interactions of nature that control the movement of matter.
The main goal of science is to reveal and explain the laws of nature, which determine all physical phenomena, in order to use them for the purposes of practical human activity.
The world is cognizable, and the process of cognition is endless. The study of the world around us has shown that matter is in constant motion. Under the movement of matter understand any change, phenomenon. Consequently, the world around us is an eternally moving and developing matter.
Physics studies the most general forms of motion of matter and their mutual transformations. Some patterns are common to all material systems, for example, the conservation of energy - they are called physical laws.
So I decided to find out what are the interesting facts surrounding us that can be explained from the point of view of physics.
Here, for example, I found information about how many times you can fold a sheet of paper.
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We have never been able to find the original source of this widespread belief: no sheet of paper can be folded twice more than seven (according to some sources - eight) times. Meanwhile, the current record for folding is 12 times. And what is more surprising, it belongs to the girl who mathematically substantiated this “mystery of the paper sheet”.
Of course, we are talking about real paper, having a finite, not zero, thickness. If you fold it carefully and to the end, excluding breaks (this is very important), then the “refusal” to fold in half is detected, usually after the sixth time. Less often - the seventh. Try doing this with a piece of notebook paper.
And, oddly enough, the limitation depends little on the size of the sheet and its thickness. That is, just take a larger thin sheet, and fold it in half, let's say 30 or at least 15 times - it doesn’t work, no matter how you fight.
In popular collections, such as "Do you know what ..." or "Amazing is nearby", this fact - that it is impossible to fold paper more than 8 times - can still be found in many places, on the Web and beyond. But is it a fact?
Let's reason. Each addition doubles the thickness of the bale. If the thickness of the paper is taken equal to 0.1 millimeters (we do not consider the size of the sheet now), then folding it in half “only” 51 times will give the thickness of the folded pack of 226 million kilometers. Which is an obvious absurdity.
World record holder Britney Gallivan and a paper tape folded in half (in one direction) 11 times (photo from mathworld.wolfram.com).
It seems that here we begin to understand where the well-known limitation of 7 or 8 times comes from (once again - we have real paper, it does not stretch to infinity and does not tear, but it will tear - this is no longer folding). But still…
In 2001, an American schoolgirl decided to come to grips with the problem of double folding, and this turned out to be a whole scientific study, and even a world record.
Actually, it all started with a challenge thrown by the teacher to the students: “But try to fold at least something in half 12 times!”. Like, make sure that this is from the category of completely impossible.
Britney Gallivan (note that she is now a student) initially reacted like Lewis Carroll's Alice: "It's useless to try." But after all, the Queen said to Alice: "I dare say that you did not have much practice."
So Gallivan took up the practice. Having suffered quite a bit with various objects, she folded a sheet of gold foil in half 12 times, which put her teacher to shame.
An example of folding a sheet in half four times. The dotted line is the previous position of the triple addition. The letters show that the points on the surface of the sheet are displaced (that is, the sheets slide relative to each other), and as a result, take a different position than it might seem at a cursory glance (illustration from pomonahistorical.org).
This girl did not calm down. In December 2001, she created a mathematical theory (well, or mathematical justification) for the process of double folding, and in January 2002 she did a 12-fold folding in half with paper, using a series of rules and several folding directions (for lovers of mathematics, a little more -).
Britney noticed that mathematicians had previously addressed this problem, but no one had yet provided a correct and proven solution to the problem.
Gallivan was the first person to correctly understand and justify the reason for the limits on addition. She studied the effects that accumulate when a real sheet is folded and the “loss” of paper (and any other material) on the fold itself. She obtained equations for the folding limit, for any given leaf parameters. Here they are.
The first equation refers to folding the strip in only one direction. L is the minimum possible length of the material, t is the thickness of the sheet, and n is the number of doubled folds. Of course, L and t must be expressed in the same units.
Gallivan and her record (photo from pomonahistorical.org).
In the second equation, we are talking about folding in different, variable directions (but still - twice each time). Here W is the width of the square sheet. The exact equation for folding in "alternative" directions is more complicated, but here is a form that gives a very realistic result.
