Of course, we are talking about real paper, which has a finite, and not zero, thickness. If you fold it carefully and completely, excluding tears (this is very important), then the “failure” to fold in half is usually detected after the sixth time. Less often - the seventh. Try this with a piece of paper from your notebook.
And, oddly enough, the limitation depends little on the size of the sheet and its thickness. That is, just take it thin sheet more, and folding it in half, since let’s say 30 or at least 15, doesn’t work, no matter how hard you try.
In popular collections such as “Did you know that...” or “The amazing thing is nearby”, this fact - that you can’t fold a piece of paper more than 8 times - can still be found in many places, online and off. But is this a fact?
Let's reason. Each fold doubles the thickness of the bale. If the thickness of the paper is taken to be 0.1 millimeters (we are not considering the size of the sheet now), then folding it in half “only” 51 times will give the thickness of the folded pack 226 million kilometers. Which is already obvious absurdity.
It seems that this is where we begin to understand where the well-known limitation of 7 or 8 times comes from (once again, our paper is real, it does not stretch indefinitely and does not tear, but if it breaks, this is no longer folding). And yet…
In 2001, one American schoolgirl decided to take a closer look at 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 something in half 12 times!” Like, make sure that this is something completely impossible.
Britney Gallivan (note that she is now a student) initially reacted like Lewis Carroll's Alice: "It's no use trying." But the Queen said to Alice: “I dare say that you haven’t had much practice.”
So Gallivan started practicing. Having suffered quite a bit with various objects, she finally folded a sheet of gold foil in half 12 times, which put her teacher to shame.
The girl did not calm down at this. In December 2001, she created a mathematical theory (or, well, a mathematical justification) for the double folding process, and in January 2002, she did a 12-fold folding in half with paper, using a number of rules and several folding directions (for math lovers, a little more detail -).
Britney noted that mathematicians had already addressed this problem before, but no one had yet provided a correct and practice-tested solution to the problem.
Gallivan became the first person to correctly understand and justify the reason for the restrictions on addition. She studied the effects that accumulate when folding a real sheet and the “loss” of paper (and any other material) to the fold itself. She obtained equations for the folding limit for any initial sheet parameters. Here they are:
The first equation applies to folding the strip in one direction only. L is the minimum possible length of the material, t is the thickness of the sheet, and n is the number of double folds made. Of course, L and t must be expressed in the same units.
In the second equation we are talking about folding in different, variable, directions (but still doubling each time). Here W is the width of the square sheet. The exact equation for folding in "alternate" directions is more complex, but here is a form that gives a very close result.
For paper that is not square, the above equation still gives a very accurate limit. If the paper is, say, 2 to 1 (in length and width), it is easy to figure out that you need to fold it once and “reduce” it to a square of double thickness, and then use the above formula, mentally keeping in mind one extra fold.
In her work, the schoolgirl defined strict rules for double addition. For example, a sheet that is folded n times must have 2n unique layers lying in a row on one line. Sections of sheets that do not meet this criterion cannot be counted as part of the folded bundle.
So Britney became the first person in the world to fold a sheet of paper in half 9, 10, 11 and 12 times. One might say, not without the help of mathematics.
On January 24, 2007, in the 72nd episode of the TV show “Mythbusters,” a team of researchers tried to refute the law. They formulated it more precisely:
Even a very large dry sheet of paper cannot be folded twice more than seven times, making each fold perpendicular to the previous one.
The law was confirmed on an ordinary A4 sheet, then the researchers tested the law on a huge sheet of paper. They managed to fold a sheet the size of a football field (51.8×67.1 m) 8 times without special means(11 times using a roller and loader). According to fans of the TV show, tracing paper from a 520×380 mm offset printing plate packaging folds eight times effortlessly when folded fairly carelessly, and nine times with effort.
Regular paper napkin folds 8 times, if you violate the condition and fold once not perpendicular to the previous one (on the video after the fourth - fifth).
Headgear also tested this theory.
| Comments: 0 |
A scientific educational program filmed in Australia by the ABC channel in 1969. The program was hosted by Julius Semner Miller, who conducted experiments related to various disciplines in physics.
Let me introduce you to one of the interesting properties of glass, which is commonly called Prince Rupert's drops (or tears). If you drop molten glass into cold water, it will harden in the shape of a drop with a long thin tail. Due to instant cooling, the drop acquires increased hardness, that is, it is not so easy to crush it. But if you break off the thin tail of such a glass drop, it will immediately explode, scattering the finest glass dust around itself.
Sergey Ryzhikov
Lectures by Sergei Borisovich Ryzhikov with demonstrations of physical experiments were given in 2008–2010 in the Large Demonstration Auditorium of the Faculty of Physics of Moscow State University. M. V. Lomonosov.
The book talks about the various connections that exist between mathematics and chess: about mathematical legends about the origin of chess, about playing machines, about unusual games on a chessboard, etc. All known types of mathematical problems and puzzles on a chess theme are covered: problems about the chessboard, about routes, strength, arrangements and permutations of pieces on it. The problems “on the move of a knight” and “on eight queens”, which were studied by the great mathematicians Euler and Gauss, are considered. Mathematical coverage of some purely chess issues is given - the geometric properties of the chessboard, the mathematics of chess tournaments, the system of Elo coefficients.
Of course, we are talking about real paper, which has a finite, and not zero, thickness. If you fold it carefully and completely, excluding tears (this is very important), then the “failure” to fold in half is usually detected after the sixth time. Less often - the seventh. Try this with a piece of paper from your notebook.
And, oddly enough, the limitation depends little on the size of the sheet and its thickness. That is, just taking a thin sheet of paper larger and folding it in half, let’s say 30 or at least 15, doesn’t work, no matter how hard you try.
In popular collections such as “Did you know that...” or “The amazing thing is nearby”, this fact - that you can’t fold a piece of paper more than 8 times - can still be found in many places, online and off. But is this a fact?
Let's reason. Each fold doubles the thickness of the bale. If the thickness of the paper is taken to be 0.1 millimeters (we are not considering the size of the sheet now), then folding it in half “only” 51 times will give the thickness of the folded pack 226 million kilometers. Which is already obvious absurdity.
It seems that this is where we begin to understand where the well-known limitation of 7 or 8 times comes from (once again, our paper is real, it does not stretch indefinitely and does not tear, but if it breaks, this is no longer folding). And yet…
In 2001, one American schoolgirl decided to take a closer look at 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 something in half 12 times!” Like, make sure that this is something completely impossible.
Britney Gallivan (note that she is now a student) initially reacted like Lewis Carroll's Alice: "It's no use trying." But the Queen said to Alice: “I dare say that you haven’t had much practice.”
So Gallivan started practicing. Having suffered quite a bit with various objects, she finally folded a sheet of gold foil in half 12 times, which put her teacher to shame.
The girl did not calm down at this. In December 2001, she created a mathematical theory (or, well, a mathematical justification) for the double folding process, and in January 2002, she did a 12-fold folding in half with paper, using a number of rules and several folding directions (for math lovers, a little more detail -).
Britney noted that mathematicians had already addressed this problem before, but no one had yet provided a correct and practice-tested solution to the problem.
Gallivan became the first person to correctly understand and justify the reason for the restrictions on addition. She studied the effects that accumulate when folding a real sheet and the “loss” of paper (and any other material) to the fold itself. She obtained equations for the folding limit for any initial sheet parameters. Here they are:
The first equation applies to folding the strip in one direction only. L is the minimum possible length of the material, t is the thickness of the sheet, and n is the number of double folds made. Of course, L and t must be expressed in the same units.
In the second equation we are talking about folding in different, variable, directions (but still doubling each time). Here W is the width of the square sheet. The exact equation for folding in "alternate" directions is more complex, but here is a form that gives a very close result.
For paper that is not square, the above equation still gives a very accurate limit. If the paper is, say, 2 to 1 (in length and width), it is easy to figure out that you need to fold it once and “reduce” it to a square of double thickness, and then use the above formula, mentally keeping in mind one extra fold.
In her work, the schoolgirl defined strict rules for double addition. For example, a sheet that is folded n times must have 2n unique layers lying in a row on one line. Sections of sheets that do not meet this criterion cannot be counted as part of the folded bundle.
So Britney became the first person in the world to fold a sheet of paper in half 9, 10, 11 and 12 times. One might say, not without the help of mathematics.
On January 24, 2007, in the 72nd episode of the TV show “Mythbusters,” a team of researchers tried to refute the law. They formulated it more precisely:
Even a very large dry sheet of paper cannot be folded twice more than seven times, making each fold perpendicular to the previous one.
The law was confirmed on an ordinary A4 sheet, then the researchers tested the law on a huge sheet of paper. They managed to fold a sheet the size of a football field (51.8x67.1 m) 8 times without special tools (11 times using a roller and a loader). According to fans of the TV show, tracing paper from a 520×380 mm offset printing plate package folds eight times effortlessly when folded fairly casually, and nine times with effort.
An ordinary paper napkin is folded 8 times, if you violate the condition and fold once not perpendicular to the previous one (on the roller after the fourth - the fifth).
Headgear also tested this theory.
| Comments: 0 |
Gubin V.B.
Mathematics studies the principles and results of activity in general, as if developing preparations for describing real activity and its results, and this is one of the sources of its universality.
Heads or tails? Under certain conditions, the outcome of a coin toss can be accurately predicted. These certain conditions, as recently shown by Polish theoretical physicists, are high accuracy in specifying the initial position and falling speed of the coin.
Caustics are ubiquitous optical surfaces and curves created by the reflection and refraction of light. Caustics can be described as lines or surfaces along which light rays are concentrated.
Richard Feynman
Imagine electric and magnetic fields. What did you do for this? Do you know how to do this? And how do I imagine electric and magnetic fields? What do I actually see? What is required of the scientific imagination? Is it any different from trying to imagine a room full of invisible angels? No, it doesn't look like such an attempt.
We present to your attention a research program that consistently revives neo-Pythagorean philosophy in theoretical physics and is based on the belief in the non-randomness of physical laws, in the existence of a single primary principle that determines the structure (visible and invisible) of the World and written in an abstract mathematical language, in the language of Numbers (integers, real and possibly their generalizations).
According to the hypothesis, our external physical reality is a mathematical structure. That is, the physical world is mathematical in a certain sense. All mathematical structures that can be calculated exist. The hypothesis suggests that worlds corresponding to different sets of initial states, physical constants, or completely different equations can be considered equally real.
Yuri Erin
It is known that the growth of giant dunes occurs due to the absorption of smaller dunes and, it would seem, nothing prevents them from taking as much as they like. large sizes. French scientists from the Laboratory of Physics and Mechanics of Heterogeneous Media, in collaboration with researchers from the USA and Algeria, managed to establish that this process is limited by the depth of the so-called near-surface atmospheric layer, which determines the nature of air flow over giant dunes.
Gordon program
What characterizes “quantum” or “non-commutative” mathematics, which was actually born along with quantum mechanics, but no one noticed? How did quantum mathematics try to reconcile two great physicists, but failed? Alexander Helemsky, Doctor of Physical and Mathematical Sciences, Professor at Moscow State University, talks about why the “real” theorem answers not only the question posed, but also a number of questions that have not yet been posed.
Golubev A.
A person, even without special physical or technical education, is undoubtedly familiar with the words “electron, proton, neutron, photon.” But many people are probably hearing the word “soliton”, which is consonant with them, for the first time. This is not surprising: although what is denoted by this word has been known for more than a century and a half, proper attention to solitons began to be paid only in the last third of the 20th century. Soliton phenomena turned out to be universal and were discovered in mathematics, fluid mechanics, acoustics, radiophysics, astrophysics, biology, oceanography, and optical engineering. What is it - a soliton?
On March 26 in Oslo, the President of the Norwegian Academy of Sciences announced the name of the winner of the Abel Prize for 2014 - analogue Nobel Prize in mathematics. It was an outstanding scientist representing Russia and the USA, Yakov Grigorievich Sinai.
Introduction
Physics is one of the greatest and most important sciences studied by man. Its presence is visible in all areas of life. It is not uncommon for discoveries in physics to change history. Therefore, great scientists and their discoveries, after years, are still interesting and significant for people. Their work is still relevant today.
Physics is a science of nature that studies the most general properties of the world around us. She studies matter (matter 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 identify and explain the laws of nature that determine all physical phenomena in order to use them for the purposes of practical human activity.
The world is knowable, and the process of learning is endless. The study of the world around us has shown that matter is in constant motion. The movement of matter is understood as any change or phenomenon. Consequently, the world around us is ever-moving and developing matter.
Physics studies the most general forms of motion of matter and their mutual transformations. Some laws are common to all material systems, for example, the conservation of energy - they are called physical laws.
So I decided to find out what they are interesting facts, surrounding us, which can be explained from the point of view of physics.
For example, I found information about how many times you can fold a sheet of paper.
Video:
Files:
- Text of work: How many times can you fold a piece of paper? Accessed January 16, 2018 1:01 pm (2.4 MB)
Expert assessment results
Expert map of the interdistrict stage 2017/2018 (Experts: 3)
Total points: 8.3
We have never been able to find the original source of this widespread belief: not a single sheet of paper can be folded twice more than seven (according to some sources, eight) times. Meanwhile, the current folding record is 12 times. And what’s more surprising is that it belongs to the girl who mathematically substantiated this “riddle of a sheet of paper.”
Of course, we are talking about real paper, which has a finite, and not zero, thickness. If you fold it carefully and completely, excluding tears (this is very important), then the “failure” to fold in half is usually detected after the sixth time. Less often - the seventh. Try this with a piece of paper from your notebook.
And, oddly enough, the limitation depends little on the size of the sheet and its thickness. That is, just taking a thin sheet larger and folding it in half, since let’s say 30 or at least 15, doesn’t work, no matter how hard you try.
In popular collections such as “Did you know that...” or “The amazing thing is nearby”, this fact - that you can’t fold a piece of paper more than 8 times - can still be found in many places, online and off. But is this a fact?
Let's reason. Each fold doubles the thickness of the bale. If the thickness of the paper is taken to be 0.1 millimeters (we are not considering the size of the sheet now), then folding it in half “only” 51 times will give the thickness of the folded pack 226 million kilometers. Which is already obvious absurdity.
It seems that this is where we begin to understand where the well-known limitation of 7 or 8 times comes from (once again - our paper is real, it does not stretch indefinitely and does not tear, but if it breaks - this is no longer folding). And yet…
In 2001, one American schoolgirl decided to take a closer look at the problem of double folding, and this turned out to be a whole scientific study, and even a world record.
Britney Gallivan (note that she is now a student) initially reacted like Lewis Carroll's Alice: "It's no use trying." But the Queen said to Alice: “I dare say that you haven’t had much practice.”
So Gallivan started practicing. Having suffered quite a bit with various objects, she finally folded a sheet of gold foil in half 12 times, which put her teacher to shame.
Actually, it all started with a challenge thrown by the teacher to the students: “But try to fold something in half 12 times!” Like, make sure that this is something completely impossible.
An example of folding a sheet in half four times. The dotted line is the previous position of 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 they do not occupy the same position as it might seem at a quick glance (illustration from the site pomonahistorical.org).
The girl did not calm down at this. In December 2001, she created a mathematical theory (or mathematical justification) for the double folding process, and in January 2002, she performed 12 folds in half with paper, using a number of rules and several folding directions.
Britney noted that mathematicians had already addressed this problem before, but no one had yet provided a correct and practice-tested solution to the problem.
Gallivan became the first person to correctly understand and justify the reason for the restrictions on addition. She studied the effects that accumulate when folding a real sheet and the “loss” of paper (and any other material) to the fold itself. She obtained equations for the folding limit for any initial sheet parameters. Here they are.
The first equation applies to folding the strip in one direction only. L is the minimum possible length of the material, t is the thickness of the sheet, and n is the number of double folds made. Of course, L and t must be expressed in the same units.
In the second equation we are talking about folding in different, variable, directions (but still doubling each time). Here W is the width of the square sheet. The exact equation for folding in "alternate" directions is more complex, but here is a form that gives a very close result.
For paper that is not square, the above equation still gives a very accurate limit. If the paper has, say, 2 to 1 proportions (in length and width), it is easy to figure out that you need to fold it once and “reduce” it to a square of double thickness, and then use the above formula, mentally keeping in mind one extra fold.
In her work, the schoolgirl defined strict rules for double addition. For example, a sheet that is folded n times must have 2n unique layers lying in a row on one line. Sections of sheets that do not meet this criterion cannot be counted as part of the folded bundle.
So Britney became the first person in the world to fold a sheet of paper in half 9, 10, 11 and 12 times. One might say, not without the help of mathematics.
