Pants are equal in all directions. 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 are equal on all sides," you see. Do you know that the Greeks in the time of Pythagoras did not wear pants? How could Pythagoras even talk about something 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 cooler 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. 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 essentially, 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?
-Twice 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, with all the numbers always gives a different answer. 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!

In one thing, you can be one hundred percent sure that when asked what the square of the hypotenuse is, any adult will boldly answer: “The sum of the squares of the legs.” This theorem is firmly planted in the minds of every educated person, but it is enough just to ask someone to prove it, and then difficulties can arise. Therefore, let's remember and consider different ways of proving the Pythagorean theorem.

Brief overview of the biography

The Pythagorean theorem is familiar to almost everyone, but for some reason the biography of the person who produced it is not so popular. We'll fix it. Therefore, before studying the different ways of proving the Pythagorean theorem, you need to briefly get acquainted with his personality.

Pythagoras - a philosopher, mathematician, thinker, originally from Today it is very difficult to distinguish his biography from the legends that have developed in memory of this great man. But as follows from the writings of his followers, Pythagoras of Samos was born on the island of Samos. His father was an ordinary stone cutter, but his mother came from a noble family.

According to legend, the birth of Pythagoras was predicted by a woman named Pythia, in whose honor the boy was named. According to her prediction, a born boy was to bring many benefits and good to mankind. Which is what he actually did.

The birth of a theorem

In his youth, Pythagoras moved to Egypt to meet the famous Egyptian sages there. After meeting with them, he was admitted to study, where he learned all the great achievements of Egyptian philosophy, mathematics and medicine.

Probably, it was in Egypt that Pythagoras was inspired by the majesty and beauty of the pyramids and created his great theory. This may shock readers, but modern historians believe that Pythagoras did not prove his theory. But he only passed on his knowledge to his followers, who later completed all the necessary mathematical calculations.

Be that as it may, today not one technique for proving this theorem is known, but several at once. Today we can only guess how exactly the ancient Greeks made their calculations, so here we will consider different ways of proving the Pythagorean theorem.

Pythagorean theorem

Before you start any calculations, you need to figure out which theory to prove. The Pythagorean theorem sounds like this: "In a triangle in which one of the angles is 90 o, the sum of the squares of the legs is equal to the square of the hypotenuse."

There are 15 different ways to prove the Pythagorean Theorem in total. This is a fairly large number, so let's pay attention to the most popular of them.

Method one

Let's first define what we have. This data will also apply to other ways of proving the Pythagorean theorem, so you should immediately remember all the available notation.

Suppose a right triangle is given, with legs a, b and hypotenuse equal to c. The first method of proof is based on the fact that a square must be drawn from a right-angled triangle.

To do this, you need to draw a segment equal to the leg in to the leg length a, and vice versa. So it should turn out two equal sides of the square. It remains only to draw two parallel lines, and the square is ready.

Inside the resulting figure, you need to draw another square with a side equal to the hypotenuse of the original triangle. To do this, from the vertices ac and sv, you need to draw two parallel segments equal to c. Thus, we get three sides of the square, one of which is the hypotenuse of the original right-angled triangle. It remains only to draw the fourth segment.

Based on the resulting figure, we can conclude that the area of ​​\u200b\u200bthe outer square is (a + b) 2. If you look inside the figure, you can see that in addition to the inner square, it has four right-angled triangles. The area of ​​each is 0.5 av.

Therefore, the area is: 4 * 0.5av + s 2 \u003d 2av + s 2

Hence (a + c) 2 \u003d 2av + c 2

And, therefore, with 2 \u003d a 2 + in 2

The theorem has been proven.

Method two: similar triangles

This formula for the proof of the Pythagorean theorem was derived on the basis of a statement from the section of geometry about similar triangles. It says that the leg of a right triangle is the mean proportional to its hypotenuse and the hypotenuse segment emanating from the vertex of an angle of 90 o.

The initial data remain the same, so let's start right away with the proof. Let us draw a segment CD perpendicular to the side AB. Based on the above statement, the legs of the triangles are equal:

AC=√AB*AD, SW=√AB*DV.

To answer the question of how to prove the Pythagorean theorem, the proof must be laid by squaring both inequalities.

AC 2 \u003d AB * HELL and SV 2 \u003d AB * DV

Now we need to add the resulting inequalities.

AC 2 + SV 2 \u003d AB * (AD * DV), where AD + DV \u003d AB

It turns out that:

AC 2 + CB 2 \u003d AB * AB

And therefore:

AC 2 + CB 2 \u003d AB 2

The proof of the Pythagorean theorem and various ways of solving it require a versatile approach to this problem. However, this option is one of the simplest.

Another calculation method

Description of different ways of proving the Pythagorean theorem may not say anything, until you start practicing on your own. Many methods involve not only mathematical calculations, but also the construction of new figures from the original triangle.

In this case, it is necessary to complete another right-angled triangle VSD from the leg of the aircraft. Thus, now there are two triangles with a common leg BC.

Knowing that the areas of similar figures have a ratio as the squares of their similar linear dimensions, then:

S avs * s 2 - S avd * in 2 \u003d S avd * a 2 - S vd * a 2

S avs * (from 2 to 2) \u003d a 2 * (S avd -S vvd)

from 2 to 2 \u003d a 2

c 2 \u003d a 2 + in 2

Since this option is hardly suitable from different methods of proving the Pythagorean theorem for grade 8, you can use the following technique.

The easiest way to prove the Pythagorean theorem. Reviews

Historians believe that this method was first used to prove a theorem in ancient Greece. It is the simplest, since it does not require absolutely any calculations. If you draw a picture correctly, then the proof of the statement that a 2 + b 2 \u003d c 2 will be clearly visible.

The conditions for this method will be slightly different from the previous one. To prove the theorem, suppose that the right triangle ABC is isosceles.

We take the hypotenuse AC as the side of the square and draw its three sides. In addition, it is necessary to draw two diagonal lines in the resulting square. So that inside it you get four isosceles triangles.

To the legs AB and CB, you also need to draw a square and draw one diagonal line in each of them. We draw the first line from vertex A, the second - from C.

Now you need to carefully look at the resulting drawing. Since there are four triangles on the hypotenuse AC, equal to the original one, and two on the legs, this indicates the veracity of this theorem.

By the way, thanks to this method of proving the Pythagorean theorem, the famous phrase was born: "Pythagorean pants are equal in all directions."

Proof by J. Garfield

James Garfield is the 20th President of the United States of America. In addition to leaving his mark on history as the ruler of the United States, he was also a gifted self-taught.

At the beginning of his career, he was an ordinary teacher at a folk school, but soon became the director of one of the higher educational institutions. The desire for self-development and allowed him to offer a new theory of proof of the Pythagorean theorem. The theorem and an example of its solution are as follows.

First you need to draw two right-angled triangles on a piece of paper so that the leg of one of them is a continuation of the second. The vertices of these triangles need to be connected to end up with a trapezoid.

As you know, the area of ​​a trapezoid is equal to the product of half the sum of its bases and the height.

S=a+b/2 * (a+b)

If we consider the resulting trapezoid as a figure consisting of three triangles, then its area can be found as follows:

S \u003d av / 2 * 2 + s 2 / 2

Now we need to equalize the two original expressions

2av / 2 + s / 2 \u003d (a + c) 2 / 2

c 2 \u003d a 2 + in 2

More than one volume of a textbook can be written about the Pythagorean theorem and how to prove it. But does it make sense when this knowledge cannot be put into practice?

Practical application of the Pythagorean theorem

Unfortunately, modern school curricula provide for the use of this theorem only in geometric problems. Graduates will soon leave the school walls without knowing how they can apply their knowledge and skills in practice.

In fact, everyone can use the Pythagorean theorem in their daily life. And not only in professional activities, but also in ordinary household chores. Let's consider several cases when the Pythagorean theorem and methods of its proof can be extremely necessary.

Connection of the theorem and astronomy

It would seem how stars and triangles can be connected on paper. In fact, astronomy is a scientific field in which the Pythagorean theorem is widely used.

For example, consider the motion of a light beam in space. We know that light travels in both directions at the same speed. We call the trajectory AB along which the light ray moves l. And half the time it takes for light to get from point A to point B, let's call t. And the speed of the beam - c. It turns out that: c*t=l

If you look at this very beam from another plane, for example, from a space liner that moves at a speed v, then with such an observation of the bodies, their speed will change. In this case, even stationary elements will move with a speed v in the opposite direction.

Let's say the comic liner is sailing to the right. Then points A and B, between which the ray rushes, will move to the left. Moreover, when the beam moves from point A to point B, point A has time to move and, accordingly, the light will already arrive at a new point C. To find half the distance that point A has shifted, you need to multiply the speed of the liner by half the travel time of the beam (t ").

And in order to find how far a ray of light could travel during this time, you need to designate half the path of the new beech s and get the following expression:

If we imagine that the points of light C and B, as well as the space liner, are the vertices of an isosceles triangle, then the segment from point A to the liner will divide it into two right triangles. Therefore, thanks to the Pythagorean theorem, you can find the distance that a ray of light could travel.

This example, of course, is not the most successful, since only a few can be lucky enough to try it out in practice. Therefore, we consider more mundane applications of this theorem.

Mobile signal transmission range

Modern life can no longer be imagined without the existence of smartphones. But how much would they be of use if they could not connect subscribers via mobile communications?!

The quality of mobile communications directly depends on the height at which the antenna of the mobile operator is located. In order to calculate how far from a mobile tower a phone can receive a signal, you can apply the Pythagorean theorem.

Let's say you need to find the approximate height of a stationary tower so that it can propagate a signal within a radius of 200 kilometers.

AB (tower height) = x;

BC (radius of signal transmission) = 200 km;

OS (radius of the globe) = 6380 km;

OB=OA+ABOB=r+x

Applying the Pythagorean theorem, we find out that the minimum height of the tower should be 2.3 kilometers.

Pythagorean theorem in everyday life

Oddly enough, the Pythagorean theorem can be useful even in everyday matters, such as determining the height of a closet, for example. At first glance, there is no need to use such complex calculations, because you can simply take measurements with a tape measure. But many are surprised why certain problems arise during the assembly process if all the measurements were taken more than accurately.

The fact is that the wardrobe is assembled in a horizontal position and only then rises and is installed against the wall. Therefore, the sidewall of the cabinet in the process of lifting the structure must freely pass both along the height and diagonally of the room.

Suppose there is a wardrobe with a depth of 800 mm. Distance from floor to ceiling - 2600 mm. An experienced furniture maker will say that the height of the cabinet should be 126 mm less than the height of the room. But why exactly 126 mm? Let's look at an example.

With ideal dimensions of the cabinet, let's check the operation of the Pythagorean theorem:

AC \u003d √AB 2 + √BC 2

AC \u003d √ 2474 2 +800 2 \u003d 2600 mm - everything converges.

Let's say the height of the cabinet is not 2474 mm, but 2505 mm. Then:

AC \u003d √2505 2 + √800 2 \u003d 2629 mm.

Therefore, this cabinet is not suitable for installation in this room. Since when lifting it to a vertical position, damage to its body can be caused.

Perhaps, having considered different ways of proving the Pythagorean theorem by different scientists, we can conclude that it is more than true. Now you can use the information received in your daily life and be completely sure that all calculations will be not only useful, but also correct.

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.

1. 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.
2. 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.
3. Pythagoras was proud of the developed theorem, because this hypothesis differs from its similar ones by the maximum amount of evidence. Important: the equation was listed in the Guinness Book of Records due to 370 truthful evidence.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.”
11. 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.
12. 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.
13. Pekka, Leibniz and several other scientists tried to prove the previously known theorem, but no one succeeded.
14. 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.
15. 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.

We hope you liked the selection of pictures - Interesting facts about the Pythagorean theorem: learn new things about the famous theorem (15 photos) online of good quality. Please leave your opinion in the comments! Every opinion matters to us.

A playful proof of the Pythagorean theorem; also in jest about a buddy's baggy trousers.

• - triplets of positive integers x, y, z satisfying the equation x2+y 2=z2...

  Mathematical Encyclopedia

• - triples of natural numbers such that a triangle, the lengths of the sides of which are proportional to these numbers, is rectangular, for example. triple of numbers: 3, 4, 5...

  Natural science. encyclopedic Dictionary

• - see Rescue rocket ...

  Marine vocabulary

• - triples of natural numbers such that a triangle whose side lengths are proportional to these numbers is right-angled...

  Great Soviet Encyclopedia

• - mil. Unchanged An expression used when listing or contrasting two facts, phenomena, circumstances ...

  Educational Phraseological Dictionary

• - From the dystopian novel "Animal Farm" by the English writer George Orwell...
• - For the first time it is found in the satire "The Diary of a Liberal in St. Petersburg" by Mikhail Evgrafovich Saltykov-Shchedrin, who so vividly described the ambivalent, cowardly position of Russian liberals - their ...

  Dictionary of winged words and expressions

• - It is said in the case when the interlocutor tried to communicate something for a long time and indistinctly, cluttering up the main idea with minor details ...

  Dictionary of folk phraseology

• - The number of buttons is known. Why is the dick cramped? - about pants and the male genital organ. . 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

• - Wed. There is no immortality of the soul, so there is no virtue, "that means everything is allowed" ... A seductive theory for scoundrels ... A braggart, but the essence is the whole: on the one hand, one cannot but confess, and on the other, one cannot but confess ...

  Explanatory-phraseological dictionary of Michelson

• - Pythagorean pants foreigner. about a gifted person. Wed This is the undoubted sage. In ancient times, he probably would have invented Pythagorean pants ... Saltykov. Motley letters...
• - From one side - from the other side. Wed There is no immortality of the soul, so there is no virtue, "it means that everything is allowed" ... A seductive theory for scoundrels .....

  Michelson Explanatory Phraseological Dictionary (original orph.)

• - 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 ...
• - ON THE ONE HAND ON THE OTHER HAND. Book...

  Phraseological dictionary of the Russian literary language

• - See RANKS -...

  IN AND. Dal. Proverbs of the Russian people

• - Zharg. school Shuttle. Pythagoras. ...

  Big dictionary of Russian sayings

"Pythagorean pants are equal in all directions" in books

11. Pythagorean pants