Pythagorean pants are equal in all directions theorem. Pythagorean pants

Some discussions amuse me immensely...

Hi what are you doing?
- Yes, I solve problems from a magazine.
-Wow! Didn't expect from you.
-What didn't you expect?
- That you will sink to problems. It seems smart, after all, but you believe in all sorts of nonsense.
-Sorry I dont understand. What do you call nonsense?
-Yes, all your math. It's obvious that it's complete bullshit.
-How can you say that? Mathematics is the queen of sciences...
-Just let's do without this pathos, right? Mathematics is not a science at all, but one continuous heap of stupid laws and rules.
-What?!
- Oh, well, don't make such big eyes, you yourself know that I'm right. No, I do not argue, the multiplication table is a great thing, it has played a significant role in the development of culture and the history of mankind. But now it's all irrelevant! And then, why complicate things? In nature, there are no integrals or logarithms, these are all inventions of mathematicians.
-Wait a minute. Mathematicians did not invent anything, they discovered new laws of the interaction of numbers, using proven tools ...
-Yes of course! And do you believe it? Don't you see what nonsense they are constantly talking about? Can you give an example?
-Yes, please.
-Yes please! Pythagorean theorem.
- Well, what's wrong with her?
-It's not like that! " Pythagorean pants on all sides are equal, "you understand. Do you know that the Greeks in the time of Pythagoras did not wear pants? How could Pythagoras even talk about what he had no idea about?
-Wait a minute. What's with the pants?
- Well, they seem to be Pythagorean? Or not? Do you admit that Pythagoras didn't have pants?
Well, actually, of course, it wasn't...
-Aha, so there is a clear discrepancy in the very name of the theorem! How then can one take seriously what it says?
-Wait a minute. Pythagoras didn't say anything about pants...
- You admit it, don't you?
- Yes... So, can I continue? Pythagoras did not say anything about trousers, and there is no need to attribute other people's nonsense to him ...
- Yeah, you yourself agree that this is all nonsense!
- I didn't say that!
- Just said. You're contradicting yourself.
-So. Stop. What does the Pythagorean theorem say?
-That all pants are equal.
-Damn, did you read this theorem at all?!
-I know.
-Where?
-I read.
-What did you read?!
-Lobachevsky.
*pause*
- Excuse me, but what does Lobachevsky have to do with Pythagoras?
- Well, Lobachevsky is also a mathematician, and he seems to be even a tougher authority than Pythagoras, you say no?
*sigh*
-Well, what did Lobachevsky say about the Pythagorean theorem?
- That the pants are equal. But this is nonsense! How can you wear pants like that? And besides, Pythagoras did not wear pants at all!
- Lobachevsky said so?!
*pause for a second, confidently*
-Yes!
- Show me where it's written.
- No, well, it's not written so directly ...
-What name has this book?
- It's not a book, it's a newspaper article. About the fact that Lobachevsky was actually a German intelligence agent... well, that's beside the point. Anyway, that's exactly what he said. He is also a mathematician, so he and Pythagoras are at the same time.
- Pythagoras didn't say anything about pants.
-Well, yes! That's what it's about. It's all bullshit.
-Let's go in order. How do you personally know what the Pythagorean theorem says?
-Oh, come on! Everyone knows this. Ask anyone, they will answer you right away.
- Pythagorean pants are not pants ...
-Oh, of course! This is an allegory! Do you know how many times I've heard this before?
-The Pythagorean theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse. And EVERYTHING!
-Where are the pants?
- Yes, Pythagoras did not have any pants !!!
- Well, you see, I'm telling you about it. All your math is bullshit.
-And that's not bullshit! Take a look yourself. Here is a triangle. Here is the hypotenuse. Here are the skates...
-Why all of a sudden it’s the legs, and this is the hypotenuse? Maybe vice versa?
-Not. Legs are two sides that form a right angle.
Well, here's another right angle for you.
- He's not straight.
-And what is he, a curve?
- No, he's sharp.
Yes, this one is sharp too.
-He's not sharp, he's straight.
- You know, don't fool me! You just call things whatever you like, just to tailor the result to what you want.
-The two short sides of a right triangle are the legs. The long side is the hypotenuse.
-And who is shorter - that leg? And the hypotenuse, then, no longer rolls? You listen to yourself from the outside, what nonsense you are talking about. In the yard of the 21st century, the flowering of democracy, and you have some kind of Middle Ages. His sides, you see, are unequal ...
There is no right triangle with equal sides...
-Are you sure? Let me draw you. Here look. Rectangular? Rectangular. And all sides are equal!
- You drew a square.
-So what?
- A square is not a triangle.
-Oh, of course! As soon as he does not suit us, immediately "not a triangle"! Do not fool me. Count yourself: one corner, two corners, three corners.
-Four.
-So what?
-It's a square.
What about a square, not a triangle? He's worse, right? Just because I drew it? Are there three corners? There is, and even here is one spare. Well, here it is, you know...
- Okay, let's leave this topic.
-Yeah, are you giving up already? Nothing to object? Are you admitting that math is bullshit?
- No, I don't.
- Well, again, great again! I just proved everything to you in detail! If all your geometry is based on the teachings of Pythagoras, which, I'm sorry, is complete nonsense ... then what can you even talk about further?
- The teachings of Pythagoras are not nonsense ...
- Well, how! And then I have not heard about the school of the Pythagoreans! They, if you want to know, indulged in orgies!
-What's the matter here...
-And Pythagoras was generally a faggot! He himself said that Plato was his friend.
-Pythagoras?!
-You didn `t know? Yes, they were all fagots. And three-legged on the head. One slept in a barrel, the other ran around the city naked ...
Diogenes slept in a barrel, but he was a philosopher, not a mathematician...
-Oh, of course! If someone climbed into the barrel, then he is no longer a mathematician! Why do we need more shame? We know, we know, we passed. But you explain to me why all sorts of fagots who lived three thousand years ago and ran without pants should be an authority for me? Why should I accept their point of view?
- Okay, leave...
- No, you listen! After all, I listened to you too. These are your calculations, calculations ... You all know how to count! And ask you something to the point, right there right away: "this is a quotient, this is a variable, and these are two unknowns." And you tell me in oh-oh-oh-general, without particulars! And without any there unknown, unknown, existential... It makes me sick, you know?
-Understand.
- Well, explain to me why twice two is always four? Who came up with this? And why am I obliged to take it for granted and have no right to doubt?
- Doubt as much as you want...
- No, you explain to me! Only without these things of yours, but normally, humanly, to make it clear.
-Two times two equals four, because two times two equals four.
- Butter oil. What did you tell me new?
-Two times two is two times two. Take two and two and put them together...
So add or multiply?
-This is the same...
-Both on! It turns out that if I add and multiply seven and eight, it will also turn out the same thing?
-Not.
-And why?
Because seven plus eight doesn't equal...
-And if I multiply nine by two, it will be four?
-Not.
-And why? Multiplied two - it turned out, but suddenly a bummer with a nine?
-Yes. Twice nine is eighteen.
-And twice seven?
-Fourteen.
-And twice five?
-Ten.
- That is, four is obtained only in one particular case?
-Exactly.
-Now think for yourself. You say that there are some rigid laws and rules for multiplication. What kind of laws can we talk about here if in each specific case a different result is obtained?!
-That's not entirely true. Sometimes the result may be the same. For example, twice six equals twelve. And four times three - too ...
-Worse! Two, six, three four - nothing at all! You can see for yourself that the result does not depend on the initial data in any way. The same decision is made in two radically different situations! And this despite the fact that the same two, which we constantly take and do not change for anything, always gives a different answer with all the numbers. Where, you ask, is the logic?
-But it's just logical!
- For you - maybe. You mathematicians always believe in all sorts of transcendental crap. And these your calculations do not convince me. And do you know why?
-Why?
-Because I I know why do you really need your math. What is she all about? "Katya has one apple in her pocket, and Misha has five. How many apples should Misha give to Katya so that they have equal apples?" And you know what I'll tell you? Misha don't owe anything to anyone give away! Katya has one apple - and that's enough. Not enough for her? Let her go to work hard, and she will honestly earn for herself even for apples, even for pears, even for pineapples in champagne. And if someone wants not to work, but only to solve problems - let him sit with his one apple and not show off!

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Jarg. school Shuttle. The Pythagorean theorem, which establishes the relationship between the areas of squares built on the hypotenuse and the legs of a right triangle. BTS, 835... Big dictionary of Russian sayings

Pythagorean pants- The comic name of the Pythagorean theorem, which arose due to the fact that the squares built on the sides of a rectangle and diverging in different directions resemble the cut of pants. I loved geometry ... and at the entrance exam to the university I even received from ... ... Phraseological dictionary of Russian literary language

Pythagorean pants- A playful name for the Pythagorean theorem, which establishes the ratio between the areas of squares built on the hypotenuse and the legs of a right-angled triangle, which looks like the cut of pants in the drawings ... Dictionary of many expressions

Foreigner: about a gifted man Cf. This is the certainty of the sage. In ancient times, he probably would have invented Pythagorean pants ... Saltykov. Motley letters. Pythagorean pants (geom.): in a rectangle, the square of the hypotenuse is equal to the squares of the legs (teaching ... ... Michelson's Big Explanatory Phraseological Dictionary

Pythagorean pants are equal on all sides- The number of buttons is known. Why is the dick cramped? (roughly) about pants and the male sexual organ. Pythagorean pants are equal on all sides. To prove this, it is necessary to remove and show 1) about the Pythagorean theorem; 2) about wide pants ... Live speech. Dictionary of colloquial expressions

Pythagorean pants (invent) foreign language. about a gifted person. Wed This is the undoubted sage. In ancient times, he probably would have invented Pythagorean pants ... Saltykov. Motley letters. Pythagorean pants (geom.): in a rectangle, the square of the hypotenuse ... ... Michelson's Big Explanatory Phraseological Dictionary (original spelling)

Pythagorean pants are equal in all directions- Joking proof of the Pythagorean theorem; also in jest about buddy's baggy trousers... Dictionary of folk phraseology

Adj., rude...

PYTHAGOREAN PANTS ARE EQUAL ON ALL SIDES (NUMBER OF BUTTONS IS KNOWN. WHY IS IT CLOSE? / TO PROVE THIS, IT IS NECESSARY TO REMOVE AND SHOW)- adj., rude ... Dictionary modern colloquial phraseological units and sayings

Exist., pl., use. comp. often Morphology: pl. what? pants, (no) what? pants for what? pants, (see) what? pants what? pants, what? about pants 1. Pants are a piece of clothing that has two short or long legs and covers lower part… … Dictionary of Dmitriev

Books

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» Honored Professor of Mathematics at the University of Warwick, a well-known popularizer of science Ian Stewart, dedicated to the role of numbers in the history of mankind and the relevance of their study in our time.

Pythagorean hypotenuse

Pythagorean triangles have a right angle and integer sides. In the simplest of them, the longest side has a length of 5, the rest are 3 and 4. There are 5 regular polyhedra in total. A fifth-degree equation cannot be solved with fifth-degree roots - or any other roots. Lattices on the plane and in three-dimensional space do not have five-lobe rotational symmetry; therefore, such symmetries are also absent in crystals. However, they can be in lattices in four-dimensional space and in interesting structures known as quasicrystals.

Hypotenuse of the smallest Pythagorean triple

The Pythagorean theorem states that the longest side of a right triangle (the proverbial hypotenuse) is related to the other two sides of that triangle in a very simple and beautiful way: the square of the hypotenuse is equal to the sum squares of the other two sides.

Traditionally, we call this theorem after Pythagoras, but in fact its history is rather vague. Clay tablets suggest that the ancient Babylonians knew the Pythagorean theorem long before Pythagoras himself; the glory of the discoverer was brought to him by the mathematical cult of the Pythagoreans, whose supporters believed that the universe was based on numerical patterns. Ancient authors attributed to the Pythagoreans - and therefore to Pythagoras - a variety of mathematical theorems, but in fact we have no idea what kind of mathematics Pythagoras himself was engaged in. We don't even know if the Pythagoreans could prove the Pythagorean Theorem, or if they simply believed it was true. Or, more likely, they had convincing data about its truth, which nevertheless would not have been enough for what we consider proof today.

Evidence of Pythagoras

The first known proof of the Pythagorean theorem is found in Euclid's Elements. This is a rather complicated proof using a drawing that Victorian schoolchildren would immediately recognize as "Pythagorean pants"; the drawing really resembles underpants drying on a rope. Literally hundreds of other proofs are known, most of which make the assertion more obvious.

// Rice. 33. Pythagorean pants

One of the simplest proofs is a kind of mathematical puzzle. Take any right triangle, make four copies of it and collect them inside the square. With one laying, we see a square on the hypotenuse; with the other - squares on the other two sides of the triangle. It is clear that the areas in both cases are equal.

// Rice. 34. Left: square on the hypotenuse (plus four triangles). Right: the sum of the squares on the other two sides (plus the same four triangles). Now eliminate the triangles

The dissection of Perigal is another puzzle piece of evidence.

// Rice. 35. Dissection of Perigal

There is also a proof of the theorem using stacking squares on the plane. Perhaps this is how the Pythagoreans or their unknown predecessors discovered this theorem. If you look at how the oblique square overlaps the other two squares, you can see how to cut the large square into pieces and then put them together into two smaller squares. You can also see right-angled triangles, the sides of which give the dimensions of the three squares involved.

// Rice. 36. Proof by paving

There are interesting proofs using similar triangles in trigonometry. At least fifty different proofs are known.

Pythagorean triplets

In number theory, the Pythagorean theorem became the source of a fruitful idea: to find integer solutions to algebraic equations. A Pythagorean triple is a set of integers a, b and c such that

Geometrically, such a triple defines a right triangle with integer sides.

The smallest hypotenuse of a Pythagorean triple is 5.

The other two sides of this triangle are 3 and 4. Here

32 + 42 = 9 + 16 = 25 = 52.

The next largest hypotenuse is 10 because

62 + 82 = 36 + 64 = 100 = 102.

However, this is essentially the same triangle with doubled sides. The next largest and truly different hypotenuse is 13, for which

52 + 122 = 25 + 144 = 169 = 132.

Euclid knew that there were an infinite number of different variations of Pythagorean triples, and he gave what might be called a formula for finding them all. Later, Diophantus of Alexandria offered a simple recipe, basically the same as Euclidean.

Take any two natural numbers and calculate:

their double product;

difference of their squares;

the sum of their squares.

The three resulting numbers will be the sides of the Pythagorean triangle.

Take, for example, the numbers 2 and 1. Calculate:

double product: 2 × 2 × 1 = 4;

difference of squares: 22 - 12 = 3;

sum of squares: 22 + 12 = 5,

and we got the famous 3-4-5 triangle. If we take the numbers 3 and 2 instead, we get:

double product: 2 × 3 × 2 = 12;

difference of squares: 32 - 22 = 5;

sum of squares: 32 + 22 = 13,

and we get the next famous triangle 5 - 12 - 13. Let's try to take the numbers 42 and 23 and get:

double product: 2 × 42 × 23 = 1932;

difference of squares: 422 - 232 = 1235;

sum of squares: 422 + 232 = 2293,

no one has ever heard of the triangle 1235-1932-2293.

But these numbers work too:

12352 + 19322 = 1525225 + 3732624 = 5257849 = 22932.

There is another feature in the Diophantine rule that has already been hinted at: having received three numbers, we can take another arbitrary number and multiply them all by it. Thus, a 3-4-5 triangle can be turned into a 6-8-10 triangle by multiplying all sides by 2, or into a 15-20-25 triangle by multiplying everything by 5.

If we switch to the language of algebra, the rule takes the following form: let u, v and k - integers. Then a right triangle with sides

2kuv and k (u2 - v2) has a hypotenuse

There are other ways of presenting the main idea, but they all boil down to the one described above. This method allows you to get all Pythagorean triples.

Regular polyhedra

There are exactly five regular polyhedra. A regular polyhedron (or polyhedron) is a three-dimensional figure with a finite number of flat faces. Facets converge with each other on lines called edges; edges meet at points called vertices.

The culmination of the Euclidean "Beginnings" is the proof that there can be only five regular polyhedra, that is, polyhedra in which each face is a regular polygon ( equal sides, equal angles), all faces are identical and all vertices are surrounded equal number equally spaced edges. Here are five regular polyhedra:

tetrahedron with four triangular faces, four vertices and six edges;

cube, or hexahedron, with 6 square faces, 8 vertices and 12 edges;

octahedron with 8 triangular faces, 6 vertices and 12 edges;

dodecahedron with 12 pentagonal faces, 20 vertices and 30 edges;

icosahedron with 20 triangular faces, 12 vertices and 30 edges.

// Rice. 37. Five regular polyhedra

Regular polyhedra can also be found in nature. In 1904, Ernst Haeckel published drawings of tiny organisms known as radiolarians; many of them are shaped like the same five regular polyhedra. Perhaps, however, he slightly corrected nature, and the drawings do not fully reflect the shape of specific living beings. The first three structures are also observed in crystals. You will not find a dodecahedron and an icosahedron in crystals, although irregular dodecahedrons and icosahedrons sometimes come across there. True dodecahedrons can occur as quasicrystals, which are like crystals in every way, except that their atoms do not form a periodic lattice.

// Rice. 38. Drawings by Haeckel: radiolarians in the form of regular polyhedra

// Rice. 39. Developments of Regular Polyhedra

It can be interesting to make models of regular polyhedra out of paper by first cutting out a set of interconnected faces - this is called a polyhedron sweep; the scan is folded along the edges and the corresponding edges are glued together. It is useful to add an additional area for glue to one of the edges of each such pair, as shown in Fig. 39. If there is no such platform, you can use adhesive tape.

Equation of the fifth degree

Does not exist algebraic formula for solving equations of the 5th degree.

AT general view The 5th equation looks like this:

ax5 + bx4 + cx3 + dx2 + ex + f = 0.

The problem is to find a formula for solving such an equation (it can have up to five solutions). Experience with square and cubic equations, as well as with equations of the fourth degree, suggests that such a formula should also exist for equations of the fifth degree, and, in theory, the roots of the fifth, third, and second degrees should appear in it. Again, one can safely assume that such a formula, if it exists, will turn out to be very, very complicated.

This assumption ultimately turned out to be wrong. Indeed, no such formula exists; at least there is no formula consisting of the coefficients a, b, c, d, e and f, composed using addition, subtraction, multiplication and division, and taking roots. Thus, there is something very special about the number 5. The reasons for this unusual behavior of the five are very deep, and it took a lot of time to figure them out.

The first sign of a problem was that no matter how hard mathematicians tried to find such a formula, no matter how smart they were, they always failed. For some time, everyone believed that the reasons lie in the incredible complexity of the formula. It was believed that no one simply could understand this algebra properly. However, over time, some mathematicians began to doubt that such a formula even existed, and in 1823 Niels Hendrik Abel was able to prove the opposite. There is no such formula. Shortly thereafter, Évariste Galois found a way to determine whether an equation of one degree or another - 5th, 6th, 7th, generally any - is solvable using this kind of formula.

The conclusion from all this is simple: the number 5 is special. You can decide algebraic equations(with help roots of the nth degrees for different values of n) for degrees 1, 2, 3 and 4, but not for the 5th degree. This is where the obvious pattern ends.

No one is surprised that equations of powers greater than 5 behave even worse; in particular, they have the same difficulty: no general formulas for their solution. This does not mean that the equations have no solutions; it also does not mean that it is impossible to find very precise numerical values for these solutions. It's all about the limitations of traditional algebra tools. This is reminiscent of the impossibility of trisecting an angle with a ruler and a compass. There is an answer, but the listed methods are not sufficient and do not allow you to determine what it is.

Crystallographic limitation

Crystals in two and three dimensions do not have 5-beam rotational symmetry.

The atoms in a crystal form a lattice, that is, a structure that repeats periodically in several independent directions. For example, the pattern on the wallpaper is repeated along the length of the roll; in addition, it is usually repeated in the horizontal direction, sometimes with a shift from one piece of wallpaper to the next. Essentially, the wallpaper is a two-dimensional crystal.

There are 17 varieties of wallpaper patterns on the plane (see chapter 17). They differ in the types of symmetry, that is, in the ways of rigidly shifting the pattern so that it lies exactly on itself in its original position. The types of symmetry include, in particular, various options rotation symmetry, where the picture should be rotated by a certain angle around a certain point - the center of symmetry.

The order of symmetry of rotation is how many times you can rotate the body to a full circle so that all the details of the picture return to their original positions. For example, a 90° rotation is 4th order rotational symmetry*. The list of possible types of rotational symmetry in the crystal lattice again points to the unusualness of the number 5: it is not there. There are variants with rotational symmetry of 2nd, 3rd, 4th and 6th orders, but no wallpaper pattern has 5th order rotational symmetry. There is also no rotational symmetry of order greater than 6 in crystals, but the first violation of the sequence still occurs at the number 5.

The same happens with crystallographic systems in three-dimensional space. Here the lattice repeats itself in three independent directions. There is 219 various types symmetry, or 230, if we consider the mirror reflection of the pattern as a separate version of it - moreover, in this case there is no mirror symmetry. Again, rotational symmetries of orders 2, 3, 4, and 6 are observed, but not 5. This fact is called the crystallographic constraint.

In four-dimensional space, lattices with 5th order symmetry exist; in general, for lattices of sufficiently high dimension, any predetermined order of rotational symmetry is possible.

// Rice. 40. Crystal lattice of table salt. Dark balls represent sodium atoms, light balls represent chlorine atoms.

Quasicrystals

While 5th order rotational symmetry is not possible in 2D and 3D lattices, it can exist in slightly less regular structures known as quasicrystals. Using Kepler's sketches, Roger Penrose discovered flat systems with more common type fivefold symmetry. They are called quasicrystals.

Quasicrystals exist in nature. In 1984, Daniel Shechtman discovered that an alloy of aluminum and manganese can form quasi-crystals; Initially, crystallographers greeted his message with some skepticism, but later the discovery was confirmed, and in 2011 Shekhtman was awarded Nobel Prize in chemistry. In 2009, a team of scientists led by Luca Bindi discovered quasi-crystals in a mineral from the Russian Koryak Highlands - a compound of aluminum, copper and iron. Today this mineral is called icosahedrite. By measuring the content of various oxygen isotopes in the mineral with a mass spectrometer, scientists showed that this mineral did not originate on Earth. It formed about 4.5 billion years ago, at a time when solar system was in its infancy, and spent most of its time in the asteroid belt orbiting the Sun until some disturbance altered its orbit and brought it eventually to Earth.

// Rice. 41. Left: one of two quasi-crystalline lattices with exact fivefold symmetry. Right: Atomic model of an icosahedral aluminum-palladium-manganese quasicrystal

Pythagorean pants The comic name of the Pythagorean theorem, which arose due to the fact that the squares built on the sides of a rectangle and diverging in different directions resemble the cut of trousers. I loved geometry ... and at the entrance exam to the university I even received praise from Chumakov, a professor of mathematics, for explaining the properties of parallel lines and Pythagorean pants without a blackboard, drawing with my hands in the air(N. Pirogov. Diary of an old doctor).

Phraseological dictionary of the Russian literary language. - M.: Astrel, AST. A. I. Fedorov. 2008 .

See what "Pythagorean pants" are in other dictionaries:

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Pythagorean pants- ... Wikipedia

Pythagorean pants- Zharg. school Shuttle. The Pythagorean theorem, which establishes the relationship between the areas of squares built on the hypotenuse and the legs of a right triangle. BTS, 835... Big dictionary of Russian sayings

Pythagorean pants (invent)- foreigner: about a gifted person Cf. This is the certainty of the sage. In ancient times, he probably would have invented Pythagorean pants ... Saltykov. Motley letters. Pythagorean pants (geom.): in a rectangle, the square of the hypotenuse is equal to the squares of the legs (teaching ... ... Michelson's Big Explanatory Phraseological Dictionary

Pythagorean pants invent- Pythagorean pants (invent) foreigner. about a gifted person. Wed This is the undoubted sage. In ancient times, he probably would have invented Pythagorean pants ... Saltykov. Motley letters. Pythagorean pants (geom.): in a rectangle, the square of the hypotenuse ... ... Michelson's Big Explanatory Phraseological Dictionary (original spelling)

Pythagorean pants are equal in all directions- Joking proof of the Pythagorean theorem; also in jest about buddy's baggy trousers... Dictionary of folk phraseology

Adj., rude...

PYTHAGOREAN PANTS ARE EQUAL ON ALL SIDES (NUMBER OF BUTTONS IS KNOWN. WHY IS IT CLOSE? / TO PROVE THIS, IT IS NECESSARY TO REMOVE AND SHOW)- adj., rude ... Explanatory dictionary of modern colloquial phraseological units and sayings

pants- noun, pl., use comp. often Morphology: pl. what? pants, (no) what? pants for what? pants, (see) what? pants what? pants, what? about pants 1. Pants are a piece of clothing that has two short or long legs and covers the bottom ... ... Dictionary of Dmitriev

Books

Pythagorean pants, . In this book you will find fantasy and adventure, miracles and fiction. Funny and sad, ordinary and mysterious... And what else is needed for entertaining reading? The main thing is to be…

The Pythagorean theorem has been known to everyone since school days. An outstanding mathematician proved a great conjecture, which is currently used by many people. The rule sounds like this: the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs. For many decades, not a single mathematician has been able to argue this rule. After all, Pythagoras walked for a long time towards his goal, so that as a result the drawings took place in everyday life.

A small verse to this theorem, which was invented shortly after the proof, directly proves the properties of the hypothesis: "Pythagorean pants are equal in all directions." This two-line was deposited in the memory of many people - to this day the poem is remembered in calculations.
This theorem was called "Pythagorean pants" due to the fact that when drawing in the middle, a right-angled triangle was obtained, on the sides of which there were squares. In appearance, this drawing resembled pants - hence the name of the hypothesis.
Pythagoras was proud of the developed theorem, because this hypothesis differs from similar ones. the maximum number evidence. Important: the equation was listed in the Guinness Book of Records due to 370 truthful evidence.
The hypothesis was proved by a huge number of mathematicians and professors from different countries in many ways. The English mathematician Jones, soon after the announcement of the hypothesis, proved it with the help of a differential equation.
At present, no one knows the proof of the theorem by Pythagoras himself. The facts about the proofs of a mathematician today are not known to anyone. It is believed that the proof of the drawings by Euclid is the proof of Pythagoras. However, some scientists argue with this statement: many believe that Euclid independently proved the theorem, without the help of the creator of the hypothesis.
Current scientists have discovered that the great mathematician was not the first to discover this hypothesis.. The equation was known long before the discovery by Pythagoras. This mathematician managed only to reunite the hypothesis.
Pythagoras did not give the equation the name "Pythagorean Theorem". This name was fixed after the "loud two-line". The mathematician only wanted the whole world to recognize and use his efforts and discoveries.
Moritz Kantor - the great greatest mathematician found and saw notes with drawings on an ancient papyrus. Shortly thereafter, Cantor realized that this theorem had been known to the Egyptians as early as 2300 BC. Only then no one took advantage of it and did not try to prove it.
Current scholars believe that the hypothesis was known as early as the 8th century BC. Indian scientists of that time discovered an approximate calculation of the hypotenuse of a triangle endowed with right angles. True, at that time no one could prove the equation for sure by approximate calculations.
The great mathematician Bartel van der Waerden, after proving the hypothesis, concluded an important conclusion: “The merit of the Greek mathematician is considered not the discovery of direction and geometry, but only its justification. In the hands of Pythagoras were computational formulas that were based on assumptions, inaccurate calculations and vague ideas. However, the outstanding scientist managed to turn it into an exact science.”
A famous poet said that on the day of the discovery of his drawing, he erected a glorious sacrifice to the bulls. It was after the discovery of the hypothesis that rumors spread that the sacrifice of a hundred bulls "went wandering through the pages of books and publications." Wits joke to this day that since then all the bulls are afraid of a new discovery.
Proof that Pythagoras did not come up with a poem about pants in order to prove the drawings he put forward: during the life of the great mathematician there were no pants yet. They were invented several decades later.
Pekka, Leibniz and several other scientists tried to prove the previously known theorem, but no one succeeded.
The name of the drawings "Pythagorean theorem" means "persuasion by speech". This is the translation of the word Pythagoras, which the mathematician took as a pseudonym.
Reflections of Pythagoras on his own rule: the secret of what exists on earth lies in numbers. After all, a mathematician, relying on his own hypothesis, studied the properties of numbers, revealed evenness and oddness, and created proportions.

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