Pi is one of the most popular mathematical concepts. Pictures are written about him, films are made, he is played on musical instruments, poems and holidays are dedicated to him, he is sought and found in sacred texts.
Who discovered pi?
Who and when first discovered the number π is still a mystery. It is known that the builders of ancient Babylon already used it with might and main when designing. On cuneiform tablets that are thousands of years old, even problems that were proposed to be solved with the help of π have been preserved. True, then it was believed that π is equal to three. This is evidenced by a tablet found in the city of Susa, two hundred kilometers from Babylon, where the number π was indicated as 3 1/8.
In the process of calculating π, the Babylonians discovered that the radius of a circle as a chord enters it six times, and they divided the circle into 360 degrees. And at the same time they did the same with the orbit of the sun. Thus, they decided to consider that there are 360 days in a year.
AT Ancient Egypt pi was 3.16.
In ancient India - 3,088.
In Italy, at the turn of the epochs, it was believed that π was equal to 3.125.
In Antiquity, the earliest mention of π refers to the famous problem of squaring the circle, that is, the impossibility of constructing a square with a compass and straightedge, the area of \u200b\u200bwhich is equal to the area of a certain circle. Archimedes equated π to the fraction 22/7.
The closest to the exact value of π came in China. It was calculated in the 5th century AD. e. famous Chinese astronomer Zu Chun Zhi. Calculating π is quite simple. It was necessary to write odd numbers twice: 11 33 55, and then, dividing them in half, put the first in the denominator of the fraction, and the second in the numerator: 355/113. The result is consistent with modern calculations of π up to the seventh digit.
Why π - π?
Now even schoolchildren know that the number π is a mathematical constant equal to the ratio of the circumference of a circle to the length of its diameter and equals π 3.1415926535 ... and further after the decimal point - to infinity.
The number acquired its designation π in a complicated way: first, this Greek letter In 1647, the mathematician Outrade named the circumference of a circle. He took the first letter of the Greek word περιφέρεια - "periphery". In 1706, the English teacher William Jones, in his Review of the Advances of Mathematics, already called the letter π the ratio of the circumference of a circle to its diameter. And the name was fixed by the 18th-century mathematician Leonhard Euler, before whose authority the rest bowed their heads. So pi became pi.
Number uniqueness
Pi is a truly unique number.
1. Scientists believe that the number of characters in the number π is infinite. Their sequence is not repeated. Moreover, no one will ever be able to find repetitions. Since the number is infinite, it can contain absolutely everything, even a Rachmaninov symphony, the Old Testament, your phone number and the year in which the Apocalypse will come.
2. π is related to chaos theory. Scientists came to this conclusion after creating Bailey's computational program, which showed that the sequence of numbers in π is absolutely random, which corresponds to the theory.
3. It is almost impossible to calculate the number to the end - it would take too much time.
4. π is an irrational number, that is, its value cannot be expressed as a fraction.
5. π is a transcendental number. It cannot be obtained by performing any algebraic operations on integers.
6. Thirty-nine decimal places in the number π is enough to calculate the length of a circle encircling known space objects in the Universe, with an error in the radius of a hydrogen atom.
7. The number π is associated with the concept of the "golden section". In the process of measuring the Great Pyramid of Giza, archaeologists found that its height is related to the length of its base, just as the radius of a circle is related to its length.
Records related to π
In 2010, Yahoo mathematician Nicholas Zhe was able to calculate two quadrillion decimal places (2x10) in π. It took 23 days, and the mathematician needed a lot of assistants who worked on thousands of computers, united by scattered computing technology. The method allowed making calculations with such a phenomenal speed. It would take more than 500 years to calculate the same on a single computer.
To simply write it all down on paper would require a paper tape over two billion kilometers long. If you expand such a record, its end will go beyond the solar system.
Chinese Liu Chao set a record for memorizing the sequence of digits of the number π. Within 24 hours and 4 minutes, Liu Chao named 67,890 decimal places without making a single mistake.
pi has a lot of fans. It is played on musical instruments, and it turns out that it “sounds” excellently. They remember it and come up with various techniques for this. For the sake of fun, they download it to their computer and brag to each other who downloaded more. Monuments are erected to him. For example, there is such a monument in Seattle. It is located on the steps in front of the Museum of Art.
π is used in decorations and interiors. Poems are dedicated to him, he is searched for in holy books and in excavations. There is even a "Club π".
In the best traditions of π, not one, but two whole days a year are devoted to the number! The first time Pi Day is celebrated on March 14th. It is necessary to congratulate each other at exactly 1 hour, 59 minutes, 26 seconds. Thus, the date and time correspond to the first digits of the number - 3.1415926.
The second time π is celebrated on July 22. This day is associated with the so-called "approximate π", which Archimedes wrote down as a fraction.
Usually on this day π students, schoolchildren and scientists arrange funny flash mobs and actions. Mathematicians, having fun, use π to calculate the laws of a falling sandwich and give each other comic awards.
And by the way, pi can actually be found in holy books. For example, in the Bible. And there the number pi is… three.
One of the most mysterious numbers known to mankind, of course, is the number Π (read - pi). In algebra, this number reflects the ratio of the circumference of a circle to its diameter. Previously, this quantity was called the Ludolf number. How and where the number Pi came from is not known for certain, but mathematicians divide the entire history of the number Π into 3 stages, into the ancient, classical and era of digital computers.
The number P is irrational, that is, it cannot be represented as a simple fraction, where the numerator and denominator are integers. Therefore, such a number has no end and is periodic. For the first time, the irrationality of P was proved by I. Lambert in 1761.
In addition to this property, the number P cannot also be the root of any polynomial, and therefore is a number property, when it was proved in 1882, it put an end to the almost sacred dispute of mathematicians “about the squaring of the circle”, which lasted for 2,500 years.
It is known that the first to introduce the designation of this number was the Briton Jones in 1706. After Euler's work appeared, the use of such a designation became generally accepted.
To understand in detail what the number Pi is, it should be said that its use is so widespread that it is difficult to even name a field of science in which it would be dispensed with. One of the simplest and most familiar values from the school curriculum is the designation of the geometric period. The ratio of the length of a circle to the length of its diameter is constant and equal to 3.14. This value was known even to the most ancient mathematicians in India, Greece, Babylon, Egypt. The earliest version of calculating the ratio dates back to 1900 BC. e. More close to contemporary meaning P was calculated by the Chinese scientist Liu Hui, in addition, he also invented a quick method for such a calculation. Its value remained generally accepted for almost 900 years.
The classical period in the development of mathematics was marked by the fact that in order to establish exactly what the number Pi is, scientists began to use the methods of mathematical analysis. In the 1400s, the Indian mathematician Madhava used the theory of series to calculate and determined the period of the number P with an accuracy of 11 digits after the decimal point. The first European, after Archimedes, who investigated the number P and made a significant contribution to its justification, was the Dutchman Ludolf van Zeulen, who already determined 15 digits after the decimal point, and wrote very entertaining words in his will: "... whoever is interested - let him go further." It was in honor of this scientist that the number P received its first and only nominal name in history.
Epoch computer computing brought new details to the understanding of the essence of the number P. So, in order to find out what the number Pi is, in 1949 the ENIAC computer was used for the first time, one of the developers of which was the future "father" of the theory of modern computers J. The first measurement was carried out for 70 hours and gave 2037 digits after the decimal point in the period of the number P. The mark of a million digits was reached in 1973. In addition, during this period, other formulas were established that reflect the number P. So, the Chudnovsky brothers were able to find one that made it possible to calculate 1,011,196,691 digits of the period.
In general, it should be noted that in order to answer the question: "What is the number Pi?", Many studies began to resemble competitions. Today, supercomputers are already dealing with the question of what it really is, the number Pi. Interesting Facts associated with these studies permeate almost the entire history of mathematics.
Today, for example, world championships are held in memorizing the number P and world records are set, the latter belongs to the Chinese Liu Chao, who named 67,890 characters in a little over a day. In the world there is even a holiday of the number P, which is celebrated as "Pi Day".
As of 2011, 10 trillion digits of the number period have already been established.
The meaning of the number "Pi", as well as its symbolism, is known all over the world. This term denotes irrational numbers (that is, their value cannot be expressed exactly as a fraction y/x, where y and x are whole numbers) and is borrowed from ancient Greek phraseological unit"peripheria", which can be translated into Russian as "circumference".The number "Pi" in mathematics denotes the ratio of the circumference of a circle to the length of its diameter. The history of the origin of the number "Pi" goes into the distant past. Many historians have tried to establish when and by whom this symbol was invented, but they failed to find out.
Pi" is a transcendental number, or by saying in simple words it cannot be a root of some polynomial with integer coefficients. It can be denoted as a real number or as an indirect number that is not algebraic.
Pi is 3.1415926535 8979323846 2643383279 5028841971 6939937510...
Pi" maybe not only irrational number, which cannot be expressed using several various numbers. The number "pi" can be represented by a certain decimal fraction, which has an infinite number of digits after the decimal point. More interesting point- all these numbers are not able to repeat.
Pi" can be correlated with the fractional number 22/7, the so-called "triple octave" symbol. This number was known even by ancient Greek priests. In addition, even ordinary residents could use it to solve any everyday problems, and also use it to design, such the most complex buildings like tombs.
According to the scientist and researcher Hayens, a similar number can be traced among the ruins of Stonehenge, and also found in the Mexican pyramids.
Pi" mentioned in his writings Ahmes, a well-known engineer at that time. He tried to calculate it as accurately as possible by measuring the diameter of a circle from the squares drawn inside it. Probably, in a certain sense, this number has a certain mystical, sacred meaning for the ancients.
Pi" in fact, is the most mysterious mathematical symbol. It can be classified as a delta, omega, etc. It is such a relationship that will be exactly the same, regardless of which point in the universe the observer will be. In addition, it will be unchanged from the measurement object.
Most likely, the first person who decided to calculate the number "Pi" using the mathematical method is Archimedes. He decided he was drawing in circles regular polygons. Considering the diameter of the circle as a unit, the scientist denoted the perimeter of the polygon drawn in the circle, considering the perimeter of the inscribed polygon as an upper estimate, but as a lower estimate of the circumference
What is the number "Pi"
The number π shows how many times the circumference of a circle is greater than its diameter. It doesn't matter what size the circle is, as it was noted at least 4 thousand years ago, the ratio always remains the same. The only question is what does it mean.
To calculate it approximately, an ordinary thread is enough. Greek Archimedes in the 3rd century BC used a more sophisticated method. He drew regular polygons inside and outside the circle. Adding up the lengths of the sides of the polygons, Archimedes more and more accurately determined the fork in which the number π is located, and realized that it was approximately equal to 3.14.
The polygon method was used for almost 2 thousand years after Archimedes, this made it possible to find out the value of the number π up to the 38th digit after the decimal point. One or two more signs - and you can calculate the length of a circle with a diameter like that of the Universe with an accuracy of an atom.
While some scientists used the geometric method, others guessed that the number pi can be calculated by adding, subtracting, dividing or multiplying other numbers. Thanks to this, the "tail" has grown to several hundred digits after the decimal point.
With the advent of the first computers and especially modern computers, accuracy increased by orders of magnitude - in 2016, the Swiss Peter Trub determined the value of the number π to 22.4 trillion decimal places. If this result is printed on a 14-point line of normal width, the entry will be slightly shorter than the average distance from Earth to Venus.
In principle, nothing prevents achieving even greater accuracy, but for scientific calculations there has long been no need for this - except perhaps for testing computers, algorithms and for research in mathematics. And there is something to explore. Even about the number π itself, not everything is known. It is proved that it is written as an infinite non-repeating fraction, that is, there is no limit to the digits after the decimal point, and they do not add up to repeating blocks. But whether numbers and their combinations appear with the same frequency is unclear. Apparently, this is so, but so far no one has provided a rigorous proof.
Further calculations are carried out mainly for sport - and for the same reason people try to remember as many digits after the decimal point as possible. The record belongs to the Indian Rajveer Mina, who in 2015 named 70 thousand characters as a keepsake, sitting blindfolded for almost ten hours.
Probably, to surpass his result, you need a special talent. But everyone is capable of simply surprising friends with a good memory. The main thing is to use one of the mnemonic techniques, which can later be useful for something else.
Structure data
The most obvious way is to split the number into identical blocks. For example, you can think of pi as a phone book with ten digit numbers, or you can think of it as a fancy history (and future) textbook that lists years. You won’t remember a lot like that, but to make an impression, a couple of tens of decimal places are enough.
Turn a number into a story
It is believed that the most convenient way remember numbers - come up with a story where they will correspond to the number of letters in words (it would be logical to replace zero with a space, but then most words will merge; instead, it is better to use words of ten letters). The phrase "Can I have a large package of coffee beans?" is based on this principle. in English:
May-3,
have-4
large - 5
container - 9
coffee - 6
beans - 5
In pre-revolutionary Russia, they came up with a similar sentence: "Whoever, jokingly and soon wishes (b) Pi to know the number, already knows (b)". Precision - up to the tenth decimal place: 3.1415926536. But it's easier to remember modern version: "She was and will be respected at work." There is also a poem: "I know this and remember it perfectly - wee, many signs are superfluous to me, in vain." And the Soviet mathematician Yakov Perelman composed a whole mnemonic dialogue:
What do I know about circles? (3.1415)
So I know the number called pi - well done! (3.1415927)
Learn and know in the number known behind the number the number, how to notice good luck! (3.14159265359)
The American mathematician Michael Keith even wrote a whole book called Not A Wake, the text of which contains information about the first 10 thousand digits of the number π.
Replace numbers with letters
Some people find it easier to remember random letters than random numbers. In this case, the numbers are replaced by the first letters of the alphabet. The first word in the title of the story Cadaeic Cadenza by Michael Keith appeared in this way. In total, 3835 digits of pi are encoded in this work - however, in the same way as in the book Not a Wake.
In Russian, for such purposes, you can use the letters from A to I (the latter will correspond to zero). How convenient it will be to remember the combinations made up of them is an open question.
Come up with images for combinations of numbers
To achieve truly outstanding results, the previous methods are no good. Record breakers use a visualization technique: images are easier to remember than numbers. First you need to match each number with a consonant letter. It turns out that each two-digit number (from 00 to 99) corresponds to a two-letter combination.
Let's say one n- this is "n", four R e - "p", pya t b - "t". Then the number 14 is "nr", and 15 is "nt". Now these pairs should be supplemented with other letters to make words, for example, " n about R a" and " n and t You will need a hundred words in total - it seems like a lot, but there are only ten letters behind them, so remembering is not so difficult.
The number π will appear in the mind as a sequence of images: three integers, a hole, a thread, etc. To better remember this sequence, images can be drawn or printed on a printer and put in front of your eyes. Some people simply lay out the relevant objects around the room and remember the numbers while looking at the interior. Regular training using this method will allow you to remember hundreds and even thousands of decimal places - or any other information, because you can visualize not only numbers.
Marat Kuzaev, Kristina Nedkova
Today is the birthday of the number Pi, which, at the initiative of American mathematicians, is celebrated on March 14 at 1 hour and 59 minutes in the afternoon. This is due to a more accurate value of Pi: we are all used 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 Mathematics and functional analysis Vladimir Zalyapin of South Ural State University says that "pi day" 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 that gives the ratio of the circumference of a circle to the diameter of a circle goes back to ancient times,” says Zalyapin. — The Sumerians and Babylonians already 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 quantity. According to the legend, Archimedes was so carried away by the calculations that he did not notice how the Roman soldiers took him hometown Syracuse. When a Roman soldier approached him, Archimedes shouted in Greek, "Don't touch my circles!" In response, the soldier stabbed him with a sword.
Plato got pretty exact value pi for its time - 3.146. Ludolf 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 was determined by the desire to get the exact value of this number. It was assumed that the number Pi is rational and, therefore, can be expressed as 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 ...), expressing the ratio of the circumference of a circle to its diameter, there are many other values \u200b\u200bof the number. Such facts are curious. In the process of measuring the dimensions of the Great Pyramid of 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 calculation error is only about 6 mm. Thirty-nine decimal places in the number Pi is enough to calculate the circumference of a circle 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 integers. This means that the sequence of decimal digits 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 know the exact value of Pi,” continues Vladimir Ilyich. But these attempts are not abandoned. In 1991 Chudnovsky achieved new 2260000000 decimal digits of the constant, and in 1994 - 4044000000. After that, the number of correct digits of the number Pi increased like an avalanche.
Chinese man holds world record for memorizing pi Liu Chao, who managed to memorize 67890 decimal places without error and reproduce them within 24 hours and 4 minutes.
About the "golden section"
By the way, the connection between "pi" and another amazing quantity - the golden ratio - has not actually been proven. People have long noticed that the "golden" proportion - it is also the Phi number - and the number Pi divided by two differ from each other by less than 3% (1.61803398... and 1.57079632...). However, for mathematics, these three percent are 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 relatives of another well-known constant - the Euler number, since the root of it is close to half the number of Pi. One second of 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
In the South Ural state university Constant's birthday is celebrated by all teachers and mathematics students. It has always been like this - it cannot be said that interest appeared only in last years. The number 3.14 is even welcomed with a special holiday concert!
