How to find reasonable information in pi. What is Pi, or how do mathematicians swear? PI number music
π = 3,
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989..
Didn't find it? Then take a look.
In general, this can be not only a phone number, but any information encoded using numbers. For example, if you present all the works of Alexander Sergeevich Pushkin in digital form, then they were stored among Pi even before he wrote them, even before he was born. In principle, they are still stored there. By the way, the curses of mathematicians in π are also present, and not only mathematicians. In a word, among Pi there is everything, even thoughts that will visit your bright head tomorrow, the day after tomorrow, in a year, or maybe in two. It is very difficult to believe in this, but even if we pretend that we believed, it will be even more difficult to get information from there and decipher it. So instead of delving into these numbers, it might be easier to approach the girl you like and ask her for the number? .. But for those who are not looking for easy ways, well, or simply interested in what the Pi number is equal to, I offer several ways to do it. calculations. Consider your health.
What is Pi equal to? Methods for calculating it:
1. Experimental method. If Pi is the ratio of the circumference of a circle to its diameter, then the first, perhaps the most obvious way to find our mysterious constant would be to manually take all measurements and calculate Pi using the formula π = l / d. Where l is the circumference and d is its diameter. Everything is very simple, you just need to arm yourself with a thread to determine the circumference, a ruler to find the diameter, and, in fact, the length of the thread itself, well, and a calculator if you have problems with long division. A saucepan or a jar of cucumbers can act as a sample to be measured, it doesn't matter, the main thing? so that there is a circle at the base.
The considered method of calculation is the simplest, but, unfortunately, it has two significant drawbacks that affect the accuracy of the pi number obtained. Firstly, the error of the measuring devices (in our case, this is a ruler with a thread), and secondly, there is no guarantee that the circle we are measuring will have the correct shape. Therefore, it is not surprising that mathematics has presented us with many other methods for calculating π, where there is no need to make accurate measurements.
2. Leibniz series. There are several infinite series that allow you to accurately calculate the number of pi up to a large number of decimal places. One of the simplest series is the Leibniz series. π = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...
Everything is simple: we take fractions with 4 in the numerator (this is what is on top) and one number from the sequence of odd numbers in the denominator (this is what is below), successively add and subtract them with each other and get the number Pi. The more iterations or repetitions of our simple actions, the more accurate the result. Simple, but not effective, by the way, it takes 500,000 iterations to get the exact value of Pi with ten decimal places. That is, we will have to divide the unfortunate four as much as 500,000 times, and in addition to this, we will have to subtract and add the results obtained 500,000 times. Want to try?
3. Nilakantha series. No time messing around with Leibniz's side? There is an alternative. The Nilakant series, although it is a little more complicated, allows us to get the desired result faster. π = 3 + 4 / (2 * 3 * 4) - 4 / (4 * 5 * 6) + 4 / (6 * 7 * 8) - 4 / (8 * 9 * 10) + 4 / (10 * 11 * 12) - (4 / (12 * 13 * 14) ... I think, if you look closely at the given initial fragment of the series, everything becomes clear, and comments are superfluous. On this we go further.
4. Monte Carlo method A rather interesting method for calculating Pi is the Monte Carlo method. He got such an extravagant name in honor of the city of the same name in the Kingdom of Monaco. And the reason for this is accident. No, it was not named by chance, the method is simply based on random numbers, and what could be more random than the numbers that appear on the roulette wheels of the Monte Carlo casino? The calculation of pi is not the only application of this method, as in the fifties it was used in the calculations of the hydrogen bomb. But let's not get distracted.
Take a square with a side equal to 2r, and write in it a circle with a radius r... Now if you put dots in a square at random, then the probability P the fact that a point hits a circle is the ratio of the areas of the circle and the square. P = S cr / S square = πr 2 / (2r) 2 = π / 4.
Now from here we express the number Pi π = 4P... It remains only to obtain experimental data and find the probability P as the ratio of hits in the circle N cr to hitting the square N square... In general, the calculation formula will look like this: π = 4N cr / N sq.
I would like to note that in order to implement this method, it is not necessary to go to a casino, it is enough to use any more or less decent programming language. Well, the accuracy of the results obtained will depend on the number of points set, respectively, the more, the more accurate. Good luck :)
Tau number (Instead of a conclusion).
People who are far from mathematics most likely do not know, but it so happened that Pi has a brother who is twice as big as it. This is the Tau number (τ), and if Pi is the ratio of the circumference to the diameter, then Tau is the ratio of this length to the radius. And today there are proposals from some mathematicians to abandon the number Pi and replace it with Tau, as it is in many ways more convenient. But so far these are only suggestions, and as Lev Davidovich Landau said: "The new theory begins to dominate when the supporters of the old die out."
March 14 is declared the day of the number "Pi", since this date contains the first three digits of this constant.
On March 14, a very unusual holiday is celebrated all over the world - Pi Day. Even from school, everyone knows it. Students are immediately explained that the number Pi is a mathematical constant, the ratio of the circumference of a circle to its diameter, which has an infinite value. It turns out that a lot of interesting facts are connected with this number.
1. The history of number has more than one millennium, almost as long as the science of mathematics has existed. Of course, the exact value of the number was not calculated immediately. Initially, the ratio of the circumference to the diameter was considered equal to 3. But over time, when architecture began to develop, a more accurate measurement was required. By the way, the number existed, but it received the letter designation only at the beginning of the 18th century (1706) and comes from the initial letters of two Greek words meaning "circle" and "perimeter". Mathematician Jones endowed the number with the letter "π", and she firmly entered mathematics already in 1737.
2. In different epochs and among different peoples, the number Pi had different meanings. For example, in Ancient Egypt it was equal to 3.1604, among the Hindus it acquired a value of 3.162, the Chinese used the number equal to 3.1459. Over time, π was calculated more and more accurately, and when computing technology, that is, a computer, appeared, it began to number more than 4 billion characters.
3. There is a legend, or rather, experts believe that the number Pi was used in the construction of the Tower of Babel. However, it was not God's wrath that caused its collapse, but incorrect calculations during construction. They say that the ancient masters were wrong. A similar version exists regarding the Temple of Solomon.
4. It is noteworthy that they tried to introduce the value of pi even at the state level, that is, through the law. In 1897, a bill was drawn up in Indiana. According to the document, pi was 3.2. However, scientists intervened in time and thus prevented the error. In particular, Professor Purdue, who was present at the legislative assembly, spoke out against the bill.
5. It is interesting that several numbers in the infinite Pi sequence have their names. So, six nines of Pi are named after an American physicist. Once Richard Feynman gave a lecture and dumbfounded the audience with a remark. He said that he would like to memorize the digits of Pi up to six nines, only to say “nine” six times at the end of the story, hinting that its meaning is rational. Whereas in reality it is irrational.
6. Mathematicians around the world do not stop conducting research related to the number Pi. It is literally shrouded in some kind of mystery. Some theorists even believe that it contains universal truth. To exchange knowledge and new information about Pi, the Pi Club was organized. It is not easy to enter it, you need to have an outstanding memory. So, those who want to become a member of the club are examined: a person must tell from memory as many signs of the number Pi as possible.
7. They even came up with various techniques for memorizing the pi after the decimal point. For example, they come up with whole texts. In them, words have the same number of letters as the corresponding decimal place. To further simplify the memorization of such a long number, poetry is composed according to the same principle. P-club members often have fun in this way, and at the same time train their memory and ingenuity. For example, Mike Keith had such a hobby, who, eighteen years ago, came up with a story, each word in which was equal to almost four thousand (3834) digits of pi.
8. There are even people who have set records for memorizing pi signs. So, in Japan, Akira Haraguchi learned by heart more than eighty-three thousand characters. But the national record is not so outstanding. A resident of Chelyabinsk was able to memorize only two and a half thousand numbers after the decimal point of Pi.
Pi in perspective
9. Pi has been celebrated for more than a quarter of a century since 1988. One day, Larry Shaw, a physicist from the popular science museum in San Francisco, noticed that March 14 coincides with the number Pi in writing. In date, month and day form 3.14.
10. Pi Day is celebrated not only in an original way, but in a fun way. Of course, scientists who study the exact sciences do not miss it. For them, this is a way not to break away from what they love, but at the same time to relax. On this day, people gather and prepare different delicacies with the image of Pi. Especially there is a place for confectioners to roam. They can make pi cakes and similar shaped cookies. After tasting the delicacies, mathematicians arrange different quizzes.
11. There is an interesting coincidence. On March 14, the great scientist Albert Einstein was born, who, as you know, created the theory of relativity. Be that as it may, physicists can also join the celebration of Pi Day.
Today is the birthday of Pi, which, at the initiative of American mathematicians, is celebrated on March 14 at 1 o'clock and 59 minutes in the afternoon. This is due to the more accurate value of Pi: we are all accustomed to counting this constant as 3.14, but the number can be continued like this: 3, 14159 ... Translating this into a calendar date, we get 03.14, 1:59.
Photo: AiF / Nadezhda Uvarova
Professor of the Department of Mathematical and Functional Analysis of the South Ural State University Vladimir Zalyapin says that the "day of Pi" should still be considered July 22, because in the European date format this day is written as 22/7, and the value of this fraction is approximately equal to the value of Pi ...
“The history of the number, which gives the ratio of the circumference to the diameter of a circle, goes back to ancient times,” says Zalyapin. - Already the Sumerians and Babylonians knew that this ratio does not depend on the diameter of the circle and is constant. One of the first mentions of the number Pi can be found in the texts Egyptian scribe Ahmes(about 1650 BC). The ancient Greeks, who borrowed a lot from the Egyptians, contributed to the development of this mysterious value. According to the legend, Archimedes was so carried away by the calculations that he did not notice how the Roman soldiers took his hometown of Syracuse. When the Roman soldier approached him, Archimedes shouted in Greek: "Don't touch my circles!" In response, the soldier stabbed him with his sword.
Plato received a fairly accurate value of pi for his time - 3.146. Ludolph van Zeilen spent most of his life calculating the first 36 digits after the decimal point of Pi, and they were engraved on his tombstone after death. "
Irrational and abnormal
According to the professor, at all times the pursuit of calculating new decimal places has been driven by the desire to obtain the exact value of this number. It was assumed that the number Pi is rational and, therefore, can be expressed by a simple fraction. And this is fundamentally wrong!
Pi is also popular because it is mystical. Since ancient times, there has been a religion of worshipers of the constant. In addition to the traditional value of pi - a mathematical constant (3.1415 ...), which expresses the ratio of the circumference of a circle to its diameter, there are many other meanings of the digit. Such facts are curious. In the process of measuring the dimensions of the Great Pyramid at Giza, it turned out that it has the same ratio of height to the perimeter of its base as the radius of a circle to its length, that is, ½ Pi.
If we calculate the length of the Earth's equator using pi to the ninth decimal place, the error in the calculations is only about 6 mm. Thirty-nine decimal places in Pi is enough to calculate the circumference encircling known space objects in the Universe, with an error no greater than the radius of a hydrogen atom!
Mathematical analysis is also involved in the study of pi. Photo: AiF / Nadezhda Uvarova
Chaos in numbers
According to a professor of mathematics, in 1767 Lambert established the irrationality of the number Pi, that is, the impossibility of representing it as a ratio of two wholes. This means that the sequence of decimal places of Pi is chaos embodied in numbers. In other words, the “tail” of decimal places contains any number, any sequence of numbers, any texts that were, are and will be, but it is not possible to extract this information!
“It is impossible to find out the exact meaning of the number Pi,” continues Vladimir Ilyich. - But these attempts are not abandoned. In 1991 Chudnovsky achieved new 2260000000 decimal places of the constant, and in 1994 - 4044000000. After that, the number of correct digits of Pi increased like an avalanche.
World record for memorizing the number Pi of a Chinese Liu Chao, who managed to memorize 67890 decimal places without error and reproduce them within 24 hours and 4 minutes.
About the "golden ratio"
By the way, the connection between pi and another amazing value - the golden ratio - has not actually been proven. People have long noticed that the "golden" proportion - it is the number of Phi - and the number of Pi divided by two, differ from each other by less than 3% (1.61803398 ... and 1.57079632 ...). However, for mathematics, these three percent is too significant a difference to consider these values identical. In the same way, we can say that the number Pi and the number Phi are related to another well-known constant - the Euler number, since the root of it is close to half of the number Pi. One second Pi is 1.5708, Phi is 1.6180, the root of E is 1.6487.
This is only part of the meaning of pi. Photo: Screenshot
Pi's birthday
At South Ural State University, the birthday of the constant is celebrated by all teachers and students of mathematics. This has always been the case - one cannot say that interest has appeared only in recent years. The number 3.14 is even greeted with a special holiday concert!
If you compare circles of different sizes, you will notice the following: the sizes of different circles are proportional. This means that when the diameter of the circle increases by a certain number of times, the length of this circle also increases by the same number of times. Mathematically, it can be written like this:
| C 1 | C 2 | ||
| = | |||
| d 1 | d 2 | (1) |
where C1 and C2 are the lengths of two different circles, and d1 and d2 are their diameters.
This ratio works in the presence of the coefficient of proportionality - the already familiar constant π. From the ratio (1), we can conclude: the circumference of a circle C is equal to the product of the diameter of this circle by the circle-independent proportionality coefficient π:
C = π d.
Also, this formula can be written in a different form, expressing the diameter d through the radius R of the given circle:
C = 2π R.
It is this formula that is a guide to the world of circles for seventh graders.
Since ancient times, people have tried to establish the value of this constant. So, for example, the inhabitants of Mesopotamia calculated the area of a circle using the formula:
Whence π = 3.
In ancient Egypt, the value for π was more accurate. In 2000-1700 BC, a scribe named Ahmes compiled a papyrus, in which we find recipes for solving various practical problems. So, for example, to find the area of a circle, he uses the formula:
| 8 | 2 | |||||
| S | = | ( | d | ) | ||
| 9 |
From what considerations did he get this formula? - Unknown. Probably on the basis of their observations, however, as did other ancient philosophers.
In the footsteps of Archimedes
Which of the two is greater than 22/7 or 3.14?
- They are equal.
- Why?
- Each of them is equal to π.
A. A. Vlasov. From the Examination Card.
Some people believe that the fraction 22/7 and chiso π are identically equal. But this is a delusion. In addition to the above incorrect answer on the exam (see epigraph), one very entertaining puzzle can also be added to this group. The assignment reads: "shift one match so that the equality is true."
The solution will be as follows: you need to form a "roof" for two vertical matches on the left, using one of the vertical matches in the denominator on the right. You will get a visual image of the letter π.
Many people know that the approximation π = 22/7 was determined by the ancient Greek mathematician Archimedes. In honor of this, such an approximation is often called the "Archimedean" number. Archimedes managed not only to establish an approximate value for π, but also to find the accuracy of this approximation, namely, to find a narrow numerical interval to which the value of π belongs. In one of his works, Archimedes proves a chain of inequalities that would look like this in a modern way:
| 10 | 6336 | 14688 | 1 | |||||||||
| 3 | < | < | π | < | < | 3 | ||||||
| 71 | 1 | 1 | 7 | |||||||||
| 2017 | 4673 | |||||||||||
| 4 | 2 | |||||||||||
can be written more simply: 3.140 909< π < 3,1 428 265...
As we see from the inequalities, Archimedes found a fairly accurate value with an accuracy of 0.002. The most surprising thing is that he found the first two decimal places: 3.14 ... It is this value that we most often use in simple calculations.
Practical use
There are two people on the train:
- Look, the rails are straight, the wheels are round.
Where does the knock come from?
- How from where? The wheels are round, but the area
circle pi er square, that's the square knocking!
As a rule, they get acquainted with this amazing number in the 6-7th grade, but they study it more thoroughly by the end of the 8th grade. In this part of the article, we will give the basic and most important formulas that will be useful to you in solving geometric problems, just for a start we will agree to take π for 3.14 for ease of calculation.
Perhaps the most famous formula among schoolchildren that uses π is the formula for the length and area of a circle. The first - the formula for the area of a circle - is written as follows:
| π D 2 | |
| S = π R 2 = | |
| 4 |
where S is the area of a circle, R is its radius, D is the diameter of the circle.
The length of a circle, or, as it is sometimes called, the perimeter of a circle, is calculated by the formula:
C = 2 π R = π d,
where C is the circumference, R is the radius, d is the diameter of the circle.
It is clear that the diameter d is equal to two radii R.
From the formula for the circumference of a circle, you can easily find the radius of a circle:
where D is the diameter, C is the circumference, R is the radius of the circle.
These are basic formulas that every student should know. Also, sometimes it is necessary to calculate the area not of the entire circle, but only of its part - the sector. Therefore, we present to you it - a formula for calculating the area of a sector of a circle. It looks like this:
| α | |||
| S | = | π R 2 | |
| 360 ˚ |
where S is the area of the sector, R is the radius of the circle, α is the central angle in degrees.
So mysterious 3.14
Indeed, it is mysterious. Because in honor of these magic numbers, they organize holidays, make films, hold public events, write poetry and much more.
For example, in 1998 a film by American director Darren Aronofsky called "Pi" was released. The film has received numerous awards.
Every year on March 14 at 1:59:26 am, people with an interest in math celebrate Pi Day. For the holiday, people prepare a round cake, sit down at a round table and discuss the number of pi, solve problems and puzzles related to pi.
Poets did not ignore this amazing number, an unknown person wrote:
You just have to try and remember everything as it is - three, fourteen, fifteen, ninety-two and six.
Let's have some fun!
We bring to your attention interesting puzzles with the number of Pi. Unravel the words that are encrypted below.
1. π R
2. π L
3. π k
Answers: 1. Feast; 2. Drank; 3. Squeak.
What is "pi" is known to absolutely everyone. But the number familiar to everyone from school arises in many situations that have nothing to do with circles. It can be found in probability theory, in the Stirling formula for calculating the factorial, in solving problems with complex numbers, and in other unexpected and far from geometry areas of mathematics. The English mathematician Augustus de Morgan once called "pi" "... the mysterious number 3.14159 ... that climbs through the door, through the window and through the roof."
This mysterious number, associated with one of the three classical problems of Antiquity - the construction of a square, the area of which is equal to the area of a given circle - entails a train of dramatic historical and curious entertaining facts.
- Some Fun Facts About Pi
- 1. Did you know that the first person to use the pi symbol for 3.14 was William Jones from Wales, and this happened in 1706.
- 2. Did you know that the world record for memorizing the number Pi was set on June 17, 2009 by the Ukrainian neurosurgeon, Doctor of Medical Sciences, Professor Andrey Slyusarchuk, who retained in his memory 30 million of its characters (20 volumes of text).
- 3. Did you know that in 1996 Mike Keith wrote a short story called "Cadeic Cadenze", in his text the length of words corresponded to the first 3834 digits of Pi.
It is believed that the holiday was invented in 1987 by the physicist from San Francisco Larry Shaw, who drew attention to the fact that March 14 (in the American spelling - 3.14) exactly at 01:59 the date and time will coincide with the first digits of Pi = 3.14159.
On March 14, 1879, the creator of the theory of relativity, Albert Einstein, was also born, which makes this day even more attractive for all lovers of mathematics.
In addition, mathematicians also note the day of the approximate value of pi, which falls on July 22 (22/7 in the European date format).
"At this time, they read eulogies in honor of the number Pi and its role in the life of mankind, paint dystopian pictures of the world without Pi, eat pies with the Greek letter Pi or with the first digits of the number itself, solve mathematical puzzles and riddles, and also dance in circles." - Wikipedia writes.
Numerically, pi starts at 3.141592 and has infinite mathematical duration.
French scientist Fabrice Bellard calculated Pi with record precision. This was reported on its official website. The latest record is about 2.7 trillion (2 trillion 699 billion 999 million 990 thousand) decimal places. The previous achievement belongs to the Japanese, who calculated the constant with an accuracy of 2.6 trillion decimal places.
It took Bellard about 103 days to compute. All calculations were carried out on a home computer, the cost of which lies in the range of 2000 euros. For comparison, the previous record was set on the T2K Tsukuba System supercomputer, which took about 73 hours to work.
Initially, the number Pi appeared as the ratio of the circumference of a circle to its diameter, so its approximate value was calculated as the ratio of the perimeter of a polygon inscribed in a circle to the diameter of this circle. Later, more advanced methods appeared. Pi is now computed using rapidly converging series, such as those proposed by Srinivas Ramanujan in the early 20th century.
Pi was first calculated in binary and then converted to decimal. This was done in 13 days. In total, 1.1 terabytes of disk space is required to store all the numbers.
Such calculations are not only of practical importance. So, now there are many unsolved problems associated with pi. The question of the normality of this number has not been resolved. For example, it is known that pi and e (base of the exponent) are transcendental numbers, that is, they are not the roots of any polynomial with integer coefficients. At the same time, however, whether the sum of these two fundamental constants is a transcendental number or not is still unknown.
Moreover, it is still not known whether all digits from 0 to 9 occur in the decimal notation of pi an infinite number of times.
In this case, an ultra-precise calculation of the number is a convenient experiment, the results of which make it possible to formulate hypotheses regarding certain features of the number.
The number is calculated according to certain rules, and for any calculation, at any place and at any time, at a certain place in the number record, there is the same digit. This means that there is a certain law according to which a certain number is put in a number in a certain place. Of course, this law is not simple, but the law still exists. And, therefore, the numbers in the number record are not random, but natural.
The number of pi is counted: PI = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ... - 4 / n + 4 / (n + 2)
Find Pi or long division:
Pairs of integers that, when divided, give a large approximation to Pi. Division was done "long" to bypass Visual Basic 6 floating point length restrictions.
Pi = 3.14159265358979323846264> 33832795028841 971 ...
Among exotic methods for calculating pi, such as using the theory of probability or prime numbers, belongs the method invented by G.A. Halperin, and called P-billiard, which is based on the original model. When two balls collide, the smallest of which is between the larger one and the wall, and the larger one moves to the wall, the number of collisions of the balls makes it possible to calculate Pi with an arbitrarily large predetermined accuracy. You just need to start the process (you can also use a computer) and count the number of balls hit. The software implementation of this model is not yet known.
In every book on entertaining mathematics, you will certainly find a history of calculating and refining the meaning of pi. At first, in ancient China, Egypt, Babylon and Greece, fractions were used for calculations, for example, 22/7 or 49/16. In the Middle Ages and the Renaissance, European, Indian and Arab mathematicians clarified the meaning of "pi" to 40 digits after the decimal point, and by the beginning of the Age of Computers the number of digits was brought to 500 by the efforts of many enthusiasts. This accuracy is of purely scientific interest (more on this below) , for practice, within the Earth, 11 signs are enough after the point.
Then, knowing that the radius of the Earth is 6400 km or 6.4 * 1012 millimeters, it turns out that we, dropping the twelfth digit "pi" after the point when calculating the length of the meridian, will be mistaken by a few millimeters. And when calculating the length of the Earth's orbit when rotating around the Sun (as you know, R = 150 * 106 km = 1.5 * 1014 mm), for the same accuracy, it is enough to use "pi" with fourteen digits after the point. The average distance from the Sun to Pluto, the most distant planet in the solar system, is 40 times the average distance from the Earth to the Sun.
To calculate the length of Pluto's orbit with an error of a few millimeters, sixteen pi is sufficient. But what is there to waste time on trifles - the diameter of our Galaxy is about 100,000 light years (1 light year is approximately equal to 1013 km) or 1018 km or 1030 mm., And in the XXVII century, 34 pi signs were obtained, which are excessive for such distances.
What is the difficulty in calculating the value of "pi"? The fact is that it is not only irrational (that is, it cannot be expressed in the fraction P / Q, where P and Q are integers), but it cannot yet be a root of an algebraic equation. A number, for example, irrational, cannot be represented by a ratio of integers, but it is the root of the equation X2-2 = 0, and for the numbers "pi" and e (Euler's constant), such an algebraic (non-differential) equation cannot be specified. Such numbers (transcendental) are calculated by considering a process and are refined by increasing the steps of the process under consideration. The “simplest” way is to inscribe a regular polygon into a circle and calculate the ratio of the polygon's perimeter to its “radius” ... pages marsu
The number explains the world
It seems that two American mathematicians managed to get closer to solving the mystery of the number pi, which represents, in a purely mathematical sense, the ratio of the circumference of a circle to its diameter, Der Spiegel reports.
As an irrational value, it cannot be represented as a completed fraction, so an infinite series of numbers follows after the decimal point. This property has always attracted mathematicians who tried to find, on the one hand, a more accurate value of pi, and on the other, its generalized formula.
However, mathematicians David Bailey of the Lawrence Berkeley National Laboratory in California and Richard Grendel of Reed College in Portland looked at the number differently - they tried to find some meaning in the seemingly chaotic series of digits after the decimal point. As a result, it was found that the combinations of the following numbers are regularly repeated - 59345 and 78952.
But so far they cannot answer the question of whether the repetition is accidental or natural. The question of the regularity of the repetition of certain combinations of numbers, and not only in the number pi, is one of the most difficult in mathematics. But now we can say something more definite about this number. The discovery paves the way for solving the number pi and, in general, for determining its essence - whether it is normal for our world or not.
Both mathematicians have been interested in pi since 1996, and since that time they had to abandon the so-called "number theory" and pay attention to "chaos theory", which is now their main weapon. Researchers construct on the basis of displaying the number pi - its most common form is 3.14159 ... - the series of numbers between zero and one - 0.314, 0.141, 0.415, 0.159 and so on. Therefore, if the number pi is really chaotic, then the series of numbers starting from zero should also be chaotic. But there is no answer to this question yet. The secret of pi, like that of its older brother, the number 42, with the help of which many researchers try to explain the secret of the universe, remains to be solved. "
Interesting data on the distribution of pi digits.
(Programming is the greatest achievement of humanity. Thanks to it, we regularly learn something that we do not need to know at all, but it is very interesting)
Calculated (for a million digits after the decimal point):
zeros = 99959,
units = 99758,
twos = 100026,
triples = 100229,
fours = 100230,
fives = 100359,
sixes = 99548,
sevens = 99800,
eights = 99985,
nines = 100106.
In the first 200,000,000,000 decimal places of Pi, numbers occurred with the following frequency:
"0" : 20000030841;
"1" : 19999914711;
"2" : 20000136978;
"3" : 20000069393
"4" : 19999921691;
"5" : 19999917053;
"6" : 19999881515;
"7" : 19999967594
"8" : 20000291044;
"9" : 19999869180;
That is, the numbers are distributed almost evenly. Why? Because according to modern mathematical concepts, with an infinite number of digits, there will be exactly equal numbers of them, besides, there will be as many ones as twos and triples put together, and even as many as all the other nine digits put together. But here to know where to stop, to seize the moment, so to speak, where they are really equal.
And one more thing - in the digits of the number Pi, one can expect the appearance of any predetermined sequence of digits. For example, the most common constellations were found in the following numbers:
01234567891: s 26,852,899,245
01234567891: s 41,952,536,161
01234567891: s 99.972.955.571
01234567891: s 102,081,851,717
01234567891: s 171,257,652,369
01234567890: s 53,217,681,704
27182818284: from 45,111,908,393 are the digits of the number e. (
There was such a joke: scientists found the last number in the Pi record - it turned out to be the number e, they almost hit)
You can search in the first ten thousand characters of Pi for your phone number or date of birth, if it does not work out, then look for 100,000 characters.
In the number 1 / Pi starting from 55,172,085,586 characters are 3333333333333, isn't it amazing?
In philosophy, the accidental and the necessary are usually opposed. So the signs of pi are random? Or are they necessary? Let's say the third digit of pi is "4". And regardless of who would calculate it, in what place and at what time he would not do it, the third sign will necessarily always be equal to "4".
The connection between the number Pi, the number Phi and the Fibonacci series. Connection of the number 3.1415916 and the number 1.61803 and the Pisa sequence.
- More interesting:
- 1. In decimal positions, Pi numbers 7, 22, 113, 355 are number 2. Fractions 22/7 and 355/113 are good approximations to Pi.
- 2. Kokhansky found that Pi is an approximate root of the equation: 9x ^ 4-240x ^ 2 + 1492 = 0
- 3. If you write the capital letters of the English alphabet clockwise in a circle and cross out the letters with symmetry from left to right: A, H, I, M, O, T, U, V, W, X, Y, then the remaining letters form groups by 3,1,4,1,6 letters.
- (A) BCDEFG (HI) JKL (M) N (O) PQRS (TUVWXY) Z
- 6 3 1 4 1
- So the English alphabet should start with the letter H, I or J, and not with the letter A :)
And so what to us? And it follows from this that in the decimal tail of the number pi, you can find any conceived sequence of numbers. Your phone number? Please, more than once (you can check here, but keep in mind that this page weighs about 300 megabytes, so you will have to wait for the download. You can download a pitiful million characters here or take a word: any sequence of digits in decimal places of pi is too early or there will be late. Any!
For more sublime readers, we can offer another example: if you encrypt all the letters with numbers, then in the decimal expansion of pi you can find all world literature and science, and the recipe for making béchamel sauce, and all the holy books of all religions. I'm not kidding, this is a strict scientific fact. After all, the sequence is INFINITE and the combinations are not repeated, therefore it contains ALL combinations of numbers, and this has already been proven. And if everything, then everything. Including those that correspond to the book you have chosen.
And this again means that it contains not only all the world literature that has already been written (in particular, those books that have been burned, etc.), but also all the books that will still WILL BE written.
It turns out that this number (the only reasonable number in the universe!) Controls our world.
The question is how to find them there ...
And on this day, Albert Einstein was born, who predicted ... but why did he not predict! ... even dark energy.
This world was shrouded in deep darkness.
Let there be light! And then Newton appeared.
But Satan did not wait long for revenge.
Einstein came - and everything became as before.
They correlate well - pi and Albert ...
Theories arise, develop and ...
The bottom line: Pi is not 3.14159265358979 ....
This is a delusion based on the erroneous postulate of identifying flat Euclidean space with the real space of the Universe.
A brief explanation of why Pi is generally not equal to 3.14159265358979 ...
This phenomenon is related to the curvature of space. The lines of force in the Universe at significant distances are not perfect straight lines, but slightly curved lines. We have already grown up to the moment of stating the fact that in the real world there are no ideally straight lines, ideally flat circles, ideal Euclidean space. Therefore, we must imagine any circle of the same radius on a sphere of much larger radius.
We are mistaken in thinking that space is flat, "cubic". The universe is not cubic, not cylindrical, much less pyramidal. The universe is spherical. The only case when a plane can be ideal (in the sense of “non-curved”) is when such a plane passes through the center of the Universe.
Of course, the curvature of a CD-ROM can be neglected, since the diameter of a CD is much less than the diameter of the Earth, especially the diameter of the Universe. But one should not neglect the curvature in the orbits of comets and asteroids. The ineradicable Ptolemaic belief that we are still at the center of the universe can cost us dear.
Below are the axioms of a flat Euclidean ("cubic" Cartesian) space and an additional axiom I have formulated for a spherical space.
Axioms of flat consciousness:
through 1 point you can draw an infinite number of straight lines and an infinite number of planes.
through 2 points you can draw 1 and only 1 straight line through which you can draw an infinite number of planes.
in the general case, no straight line and one, and only one, plane cannot be drawn through 3 points. Additional axiom for spherical consciousness:
in the general case, no straight line, no plane and one and only one sphere cannot be drawn through 4 points. Arsentiev Alexey Ivanovich
A bit of mysticism. PI Number Reasonable?
Any other constant can be defined through the number Pi, including the fine structure constant (alpha), the constant of the golden ratio (f = 1.618 ...), not to mention the number e - that is why the number pi is found not only in geometry, but also in theory of relativity, quantum mechanics, nuclear physics, etc. Moreover, scientists have recently established that it is through Pi that it is possible to determine the location of elementary particles in the Table of elementary particles (previously they tried to do this through the Woody Table), and the message that in the recently deciphered human DNA the number Pi is responsible for the very structure of DNA (enough complex, it should be noted), had the effect of a bomb exploding!
According to Dr. Charles Cantor, under whose leadership the DNA was deciphered: "It seems that we have come to a solution to some fundamental problem that the universe has given us. Pi is everywhere, it controls all the processes we know, while remaining unchanged! Who does Pi itself control? There is no answer yet. "
In fact, Kantor is disingenuous, the answer is, it is simply so incredible that scientists prefer not to bring it out to the general public, fearing for their own lives (more on that later): Pi controls itself, it is reasonable! Nonsense? Do not hurry. After all, Fonvizin said that "in human ignorance it is very comforting to consider everything as nonsense that you do not know."
First, conjectures about the reasonableness of numbers in general have long been visited by many well-known mathematicians of our time. The Norwegian mathematician Niels Henrik Abel wrote to his mother in February 1829: "I received confirmation that one of the numbers is reasonable. I spoke to him! But it scares me that I cannot determine what this number is. But maybe that's for the best. The number warned me that I would be punished if It was revealed. " Who knows, Niels would have revealed the meaning of the number that spoke to him, but on March 6, 1829, he was gone.
1955, Japanese Yutaka Taniyama hypothesizes that "a certain modular shape corresponds to each elliptic curve" (as you know, on the basis of this hypothesis, Fermat's theorem was proved). On September 15, 1955, at the International Mathematical Symposium in Tokyo, where Taniyama announced his hypothesis, to a journalist's question: "How did you come up with this?" - Taniyama replies: "I didn't think of it, the number told me about it by phone." The journalist, thinking it was a joke, decided to "support" it: "Did it give you the phone number?" To which Taniyama replied seriously: "It seems that this number has been known to me for a long time, but I can now report it only after three years, 51 days, 15 hours and 30 minutes." In November 1958, Taniyama committed suicide. Three years, 51 days, 15 hours and 30 minutes - this is 3.1415. Coincidence? May be. But - here's another, even stranger. The Italian mathematician Sella Quitino, too, for several years, as he himself vaguely expressed himself, "kept in touch with one cute number." The figure, according to Kvitino, who was already in a psychiatric hospital then, "promised to say her name on her birthday." Could Kvitino have lost his mind enough to call the number Pi a number, or was he so deliberately confusing doctors? It is not clear, but on March 14, 1827, Kvitino died.
And the most mysterious story is associated with the "great Hardy" (as you all know, this is what contemporaries called the great English mathematician Godfrey Harold Hardy), who, together with his friend John Littlewood, is famous for his works in number theory (especially in the field of Diophantine approximations) and function theory ( where friends became famous for researching inequalities). As you know, Hardy was officially unmarried, although he said more than once that he was "betrothed to the queen of our world." His fellow scientists have more than once heard him talking to someone in his office, no one has ever seen his interlocutor, although his voice - metallic and slightly creaky - has long been the talk of the town at Oxford University, where he has worked in recent years. ... In November 1947, these conversations cease, and on December 1, 1947, Hardy is found in a city dump, with a bullet in his stomach. The version of suicide was confirmed by a note, where it was written in Hardy's hand: "John, you took the queen away from me, I do not blame you, but I can no longer live without her."
Is this story related to pi? It is not yet clear, but is it not, curious?
Generally speaking, there are a lot of such stories to dig up, and, of course, not all of them are tragic.
But, let's move on to the "second": how can a number be reasonable at all? It's very simple. The human brain contains 100 billion neurons, the number of pi decimal places generally tends to infinity, in general, according to formal signs, it can be reasonable. But if you believe the work of American physicist David Bailey and Canadian mathematicians Peter Borvin and Simon Ploeu, the sequence of decimal places in Pi obeys chaos theory, roughly speaking, the number Pi is chaos in its original form. Can chaos be reasonable? Of course! Just like the vacuum, with its seeming emptiness, as you know, it is by no means empty.
Moreover, if you wish, you can represent this chaos graphically - to make sure that it can be reasonable. In 1965, the American mathematician of Polish origin Stanislaw M. Ulam (he was the one who owns the key idea of the construction of a thermonuclear bomb), attending one very long and very boring (according to him) meeting, in order to somehow have fun, he began to write numbers on checkered paper included in the number Pi. Putting 3 in the center and moving in a spiral counterclockwise, he wrote out 1, 4, 1, 5, 9, 2, 6, 5 and other numbers after the decimal point. Without any second thought, along the way, he circled all the prime numbers in black circles. Soon, to his surprise, the circles began to line up along the straight lines with amazing tenacity - what happened was very similar to something reasonable. Especially after Ulam generated a color picture based on this drawing using a special algorithm.
Actually, this picture, which can be compared with both the brain and the stellar nebula, can be safely called the "Pi brain". With the help of such a structure, this number (the only reasonable number in the universe) controls our world. But - how does this management take place? As a rule, with the help of the unwritten laws of physics, chemistry, physiology, astronomy, which are controlled and corrected by a reasonable number. The above examples show that a reasonable number is also deliberately personified, communicating with scientists as a kind of superpersonality. But if so, did the number Pi come to our world in the guise of an ordinary person?
Complex issue. Maybe it came, maybe not, there is no reliable method for determining this and cannot be, but if this number is in all cases determined by itself, then we can assume that it came to our world as a person on the day corresponding to its meaning. Of course, Pi's ideal date of birth is March 14, 1592 (3.141592), however, there is no reliable statistics for this year - it is only known that it was in this year that George Villiers Buckingham was born on March 14 - Duke of Buckingham from " Three Musketeers ". He was great at fencing, he knew a lot about horses and falconry - but was he Pi? Unlikely. Duncan MacLeod, who was born on March 14, 1592, in the Highlands of Scotland, could ideally apply for the role of the human embodiment of Pi, if he were a real person.
But after all, the year (1592) can be determined by its own, more logical chronology for Pi. If we accept this assumption, then there are many more candidates for the role of pi.
The most obvious of these is Albert Einstein, born March 14, 1879. But 1879 is 1592 relative to 287 BC! Why 287? Because it was in this year that Archimedes was born, who for the first time in the world calculated the number Pi as the ratio of the circumference to the diameter and proved that it is the same for any circle! Coincidence? But aren't there many coincidences, what do you think?
In what personality Pi is personified today, it is not clear, but in order to see the meaning of this number for our world, you do not need to be a mathematician: Pi is manifested in everything that surrounds us. And this, by the way, is very characteristic of any intelligent creature, which, no doubt, is Pi!
What is a PIN?
Per-SONAL IDEN-tifi-KA-TsI-onny number.
What is PI number?
Decoding the number PI (3, 14 ...) (pin-code), anyone can do it without me, through the Glagolitsa. We substitute letters instead of numbers (the numerical values of the letters are given in Glagolitic) and we get the following phrase: Verbs (verb, say, do) Az (I, ace, master, creator) Good. And if we take the following figures, then it turns out something like the following: "I do good, I am Fita (hidden, illegitimate child, immaculate conception, unmanifest, 9), I know (know) distortion (evil) this is speaking (action) will ( desire) The earth I do I do I do I do I do the Will good I do evil (distortion) I know evil I do good "..... and so on ad infinitum, there are many numbers, but I believe that everything is about the same ...
PI number music
