What does the pi sign mean. Calculation with the desired accuracy of pi
People passionate about mathematics around the world every year eat on a piece of the fourteenth cake of March - after all, this is the day of the number Pi, the most famous irrational number. This date is directly related to the number, the first numbers of which 3.14. Pi is the ratio of the circumference of the circle to the diameter. Since it is irrational, write it in the form of a fraction is impossible. This is an infinitely long number. He was discovered thousands of years ago and since then they are constantly studying, but did they have any secrets? From ancient origin to an indefinite future here is a few most interesting facts about the number of pi.
Memorization of p.
The record in the memorization of the number after the comma belongs to Rajvir mine from India, which was able to remember 70,000 digits - he set the record twenty-first of March 2015. Before that, the record holder was Chao Lu from China, which was able to remember 67,890 digits - this record was delivered in 2005. The unofficial record holder is Akira Haragii, who recorded its repetition of 100,000 digits in the video in 2005 and not so long ago, which he managed to remember 117,000 digits. The official record would only be in the event that this video was recorded in the presence of a representative of the Guinness Book of Records, and without confirmation it remains only an impressive fact, but is not considered an achievement. Mathematics enthusiasts love to learn the pi digit. Many people use various mnemonic techniques, for example, poems, where the number of letters in each word coincides with the pi numbers. In each language, there are similar options for these phrases that help remember both the first few digits and a complete hundred.
There is a language p
The mathematics enthusized to the literature invented a dialect in which the number of letters in all words corresponds to the pi numbers in exact order. The writer Mike Keith even wrote a book not a wake, which is fully created in the PI language. Enthusiasts of such creativity write their works in full compliance with the number of letters value of numbers. It has no applied application, but is a fairly common and known phenomenon in circles of enthusiastic scientists.
Exponential growth
Pi is an infinite number, so people by definition will never be able to establish accurate numbers of this number. However, the number of numbers after the comma has greatly increased since the first use of PI. We used Babylonians, but they had enough fraction in three integers and one eighth. The Chinese and the creators of the Old Testament were limited to the top three. By 1665, Sir Isaac Newton calculated 16 digits pi. By 1719, the French mathematician Tom Pante de Lanya calculated 127 digits. The appearance of computers radically improved human knowledge about Pi. From 1949 to 1967 famous person The figures rapidly increased from 2037 to 500,000. Not so long ago, Peter Trourb, a scientist from Switzerland, was able to calculate 2.24 trillion digits of Pi! It took 105 days. Of course, this is not the limit. It is likely that with the development of technologies it will be possible to establish more accurate digit - Since Pi is infinite, the limit of accuracy simply does not exist, and only the technical features of computing equipment can limit it.
Hit Manual calculation
If you want to find a number yourself, you can use old-fashioned technique - you will need a ruler, bank and rope, you can also use the transport and pencil. The minus of the use of banks is that it should be round, and the accuracy will be determined how well the person can wind up the rope around it. You can draw a circle with transport, but it also requires skills and accuracy, since the uneven circle can seriously distort your measurements. A more accurate method involves the use of geometry. Divide the circle into a plurality of segments as pizza on pieces, and then calculate the length of the straight line, which would turn each segment into an anoscele triangle. The sum of the parties will give an approximate number Pi. The more segments you use, the more accurate the number will be. Of course, in its calculations you will not be able to get closer to the results of the computer, however, these simple experiments make it possible to understand more detail that in general is the number Pi and how it is used in mathematics. 
Opening P.
Ancient Babylonians knew about the existence of the number of Pi already four thousand years ago. Babylonian signs are calculated by PI as 3,125, and in the Egyptian mathematical papyrus there is a number 3,1605. In the Bible, the PP number is given in an outdated length - in the elbows, and the Greek mathematician Archimedes used to describe the PI Theorem of Pythagora, the geometric ratio of the length of the side of the triangle and the area of \u200b\u200bfigures inside and outside the circles. Thus, it is safe to say that PI is one of the most ancient mathematical concepts, at least the exact name of this number and appeared relatively recently.
New look at pi
Even before the number of PI has become correlated with circles, mathematicians have already many ways even for the name of this number. For example, in ancient textbooks in mathematics, you can find a phrase on Latin, which can be roughly translated as "the amount that shows the length when the diameter is multiplied with it." The irrational number became famous when the Swiss scientist Leonard Euler used him in his works on trigonometry in 1737. Nevertheless, the Greek symbol for Pi was still not used - this happened only in the book of the less famous Mathematics William Jones. He used him already in 1706, but this remained without attention. Over time, scientists have accepted such a name, and now it is the most famous version of the name, although it was also called a ludolphic number.
Is the number of pi?
The number Pi is definitely strange, but how much does it obey normal mathematical laws? Scientists have already allowed many issues related to this irrational number, but some riddles remain. For example, it is not known how often all the numbers are used - the numbers from 0 to 9 should be used in equal proportion. However, according to the first trillions, the figures are traced, but due to the fact that the number is infinite, it is impossible to prove it. There are other problems that still elude scientists. It is possible that further development Science will help shed light on them, but at the moment it remains outside the human intelligence.
Pi sounds divine
Scientists cannot respond to some questions about the number of pi, nevertheless every year they are all better understanding his essence. Already in the eighteenth century, the irrationality of this number was proved. In addition, it was proved that the number is transcendental. This means that there is no certain formula that would calculate PI with rational numbers. 
Dissatisfaction with the number of P.
Many mathematics are just in love with Pi, but there are those who believe that these numbers have no particular importance. In addition, they assure that the number of Tau, which is two times more pi, more convenient to use as irrational. Tau shows the link of the length of the circle and radius, which, according to some, is a more logical calculus method. However, it is impossible to unambiguously determine anything in this matter, and one and another number will always have supporters, both methods have the right to life, so it's just an interesting fact, and not a reason to think that you should not use the number of pi.
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1. The relevance of work.
In an infinite set of numbers, as among the stars of the universe, there are separate numbers and the integers of their "constellation" of amazing beauty, the number with the extraordinary properties and peculiar, only inherent in the harmony. We just need to be able to see these numbers, notice their properties. Peer in a natural number of numbers - and you will find in it a lot of amazing and amazing, funny and serious, unexpected and curious. Sees one who looks. After all, people and the summer starry night will not notice ... radiance. Polar Star, if you do not send your eyes into a cloudless compensation.
Returning from class to class I became acquainted with natural, fractional, decimal, negative, rational. This year I studied irrational. Among the irrational numbers there is a special number, the exact calculations of which scientists have been involved in many centuries. It met me in grade 6 when studying the topic "Circle Length and Circle Square". Attention was focused on the fact that quite often we will meet with him in class lessons in high school. Interesting were practical tasks To find the numeric value of the number π. The number π is one of interesting numbersfound when studying mathematics. It is found in different school disciplines. With the number π, many interesting facts are associated, so it causes interest in learning.
Hearing a lot of interesting things about this number, I myself decided to learn additional literature and search on the Internet to learn as much information about it and answer the problematic questions:
How long have people knew about the number of pi?
What does it need to study?
What interesting facts are connected with it
Is it true that the value of Pi is equal to approximately 3.14
Therefore, I set up target: Investigate the history of the number π and the significance of the number π at the present stage of the development of mathematics.
Tasks:
Explore the literature in order to obtain information about the history of the number π;
Set some facts from " modern biography»Numbers π;
Practical calculation of the approximate value of the circumference length ratio to the diameter.
Object of study:
Object of study: PI number.
Subject of study: Interesting facts associated with the number of pi.
2. The main part. Amazing number π.
No other number is so mysterious as "Pi" with his famous never ending numerical next. In many areas of mathematics and physics, scientists use this number and its laws.
Few of the number of all the numbers used in mathematics in natural sciences, in engineering and in everyday lifeis paying so much attention as the number of pi is given. In one book it is said: "The number Pi captures the minds of the geniuses of science and fans mathematicians around the world" ("Fractals for the classroom").
It can be found in probability theory, in solving problems with complex numbers and other unexpected and far from the geometry of mathematics regions. English Mathematician August de Morgan called somehow "PI" "... mysterious number 3,14159 ..., which climbs into the door, in the window and through the roof. " This mysterious number associated with one of the three classical antiquity tasks is to build a square whose area is equal to the area of \u200b\u200bthe specified circle - entails a train of dramatic historical and curious entertaining facts.
Some even consider it one of the five most important numbers in mathematics. But, as noted in the book "Fractals for the classroom", with all the importance of the number of PI "It is difficult to find spheres in scientific calculations, where more than twenty decimal plates would need."
3. The concept of the number of pi
The number π is a mathematical constant expressing the ratio of the circumference length to the length of its diameter. Number π (pronounced "PI") - Mathematical constant, expressing the ratio of the circumference length to the length of its diameter. Denotes letter greek alphabet "PI".
In digital expression π begins as 3,141,592 and has an infinite mathematical duration.
4. History of the number "PI"
According to experts, this number was opened by Babylonian magicians.. It was used in the construction of the famous Babylonian tower. However, not enough accurate calculus of the PI value led to the collapse of the entire project. It is possible that this mathematical constant was at the heart of the construction of the legendary temple of King Solomon.
The history of the number of PI, expressing the ratio of the circumference of its diameter, began in Ancient Egypt. Circle area diameter d. Egyptian mathematics were determined as (D-D / 9) 2 (This entry is given here in modern characters). From the above expression, it can be concluded that at that time the number P was considered equal to the fraction (16/9) 2 , or 256/81 . π = 3,160...
In the Holy Book of Jainism (one of the most ancient religions, existing in India and arising in the VI century BC) there is an indication of which it follows that the number P at that time was taken equal, which gives a fraction 3,162... Ancient Greeks Evdox, Hippocrat And other measurement of the circle reduced to the construction of the segment, and the measurement of the circle - to the construction of an equilibrium square. It should be noted that for many centuries of mathematics different countries And the peoples tried to express the ratio of the circumference of the circumference to the diameter of the rational number.
Archimedes in the III century. BC. justified in his small work "Measurement of the Circle" three positions:
Everybody isometric rectangular trianglewhose nuts are respectively equal to the length of the circle and its radius;
Circle area belongs to a square built on diameter as 11 to 14.;
The ratio of any circumference to its diameter is less 3 1/7 and more 3 10/71 .
By accurate calculations Archimedes The ratio of the circumference to the diameter is concluded between numbers 3*10/71 and 3*1/7 , which means that π = 3,1419... True meaning of this relationship 3,1415922653... In V c. BC. Chinese mathematician Tzu Chunchzhi A more accurate value of this number was found: 3,1415927...
In the first half of the XV century. Observatory Ulugbeck, near Samarkand, astronomer and mathematician al-Kashi. Calculated Pi with 16 decimal signs. Al-Kashi.produced unique calculations that were needed to compile the sinus table in increments in 1" . These tables played an important role in astronomy.
After a century and a half in Europe F. Viet. Found the number of pi only with 9 right decimal signs, making 16 doubling among the parties of polygons. But at the same time F. Viet. The first noted that PI can be found using the limits of some rows. This discovery had a big
value, as it allowed to calculate the pi with any accuracy. Only in 250 years after al-Kashi. His result was surpassed.
Birthday number ".
Unofficial holiday The "day of PI" is celebrated on March 14, which in the US format (day / number) is recorded as 3/14, which corresponds to the approximate value of the number of PI.
There is an alternative holiday option - July 22. It is called "the day of the approximate number Pi". The fact is that the presentation of this date in the form of a fraction (22/7) also gives the number of pi in the form of the result. It is believed that the holiday came up in 1987 a physicist from San Francisco Larry Show, who turned attention to that, the date and time coincide with the first discharges of the number π.
Interesting facts associated with the number ""
Scientists of Tokyo University under the guidance of Professor Yasumas Canada managed to put the world record in the calculations of the pi number up to a 12411th trillion sign. For this, the group of programmers and mathematicians needed a special program, supercomputer and 400 hours of machine time. (Guinness Book of Records).
The German King Friedrich second was so fascinated by this number that he dedicated him to him ... The whole palace of Castell del Monte, in the proportions of which can be calculated Pi. Now magic Palace Located under the protection of UNESCO.
How to remember the first digits of the number ".
Three first numbers numbers \u003d 3.14 ... Remember quite easy. And to memorize a larger number of signs there are funny sayings and poems. For example, such:
You only need to try
And remember everything as it is:
Ninety two and six.
S. Bobrov. "Magic Dvurog"
The one who learns these Quarters will always be able to name 8 characters of the number :
In the following phrases, the signs of the number can be determined by the number of letters in each word:
“What do I know about circles? " (3,1416);
“So I know the number referred to as Pi. - Well done!"
(3,1415927);
“Learn and know among the digit known for the figure as good luck to notice "
(3,14159265359)
5. Designation of the number Pi
The first introduced the designation of the length of the circumference of the circumference to the diameter of the modern symbol of Pi English Mathematician U.jonson In 1706, as a symbol, he took the first letter of the Greek word "Periferia"that translated means "circle". Introduced U.Juson The designation was commonly used after publishing L.Aelerawho used the introduced symbol for the first time in 1736 G.
At the end of the XVIII century. A.M. Lazhandr Based on work I.G.luberta Proved that the number Pi is irrational. Then the German mathematician F.Londemanrelying on research Sh.Ermita, I found strict proof that this number is not only irrational, but also transcendentally, i.e. There can be no root of an algebraic equation. The search for accurate expression pi continued after work F. Viet.. IN beginning of XVII in. Dutch mathematician from Cologne Ludolf Wang Ceilen (1540-1610) (some historians call it L.V. Kalen) Found 32 correct signs. Since then (year of publication 1615) The value of the number P with 32 decimal signs received the name of the number Ludolfa.
6. How to remember the number "pi" up to eleven signs
The number "PI" is the ratio of the circumference of the circumference to its diameter, it is expressed by an infinite decimal fraction. In everyday life, it is enough for us to know three signs (3.14). However, some calculations need great accuracy.
Our ancestors did not have computers, calculators and reference books, but since the time of Peter I they were engaged in geometric calculations in astronomy, in mechanical engineering, in a ship business. Subsequently, electrical engineering was added here - there is the concept of a "circular frequency of alternating current". For memorization of the number "Pi", two-bedned (unfortunately, we do not know the author and the place of the first publication of it; but in the late 40s of the twentieth century, Moscow schoolchildren were engaged in the textbook of Kiselev's geometry, where it was given).
The biennial is written according to the rules of the old Russian spelling, according to which after consonant In the end of the word was necessarily put "soft" or "solid" sign. Here it is, it is a wonderful historical two-deck:
Who is joking and soon wishes
"PI" know the number - I know.
The one who is going to in the future to engage in accurate calculations makes sense to remember it. So what is the number "Pi" with an accuracy of eleven signs? Count the number of letters in each word and write these numbers in a row (the first digit is separated by the semicolon).
Such accuracy is already quite enough for engineering calculations. In addition to the old, there is a modern way to memorize, which pointed to the reader, called George:
So that we are wrong
Need to read correctly:
Three, fourteen, fifteen
Ninety two and six.
It is only necessary to try
And remember everything as it is:
Three, fourteen, fifteen
Ninety two and six.
Three, fourteen, fifteen
Nine, two, six, five, three, five.
To engage in science,
Everyone should know.
You can just try
And often repeat:
"Three, fourteen, fifteen
Nine, twenty six and five. "
Well, the mathematics using modern computers can calculate almost any number of signs of the number "PI".
7. Record to memorization of the number Pi
Remember signs of pi humanity is trying for a long time. But how to put in memory infinity? Favorite question mnemonic professionals. A variety of unique theories and techniques of mastering a huge amount of information have been developed. Many of them are tested on Pi.
The world record established in the past century in Germany - 40,000 characters. The Russian record of the values \u200b\u200bof the number of Pi on December 1, 2003 in Chelyabinsk installed Alexander Belyaev. For an hour and a half with small breaks on the school board, Alexander wrote 2500 digits of the number Pi.
Prior to this, a record in Russia was considered to list 2000 signs, which was managed to be made in 1999 in Yekaterinburg. According to Alexander Belyaeva, the head of the center for the development of shaped memory, such an experiment with its memory can carry out any of us. It is just important to know special memorization techniques and periodically train.
Conclusion.
The number pi appears in the formulas used in many areas. Physics, electrical engineering, electronics, probability theory, construction and navigation are just some of them. And it seems that, just as there is no end of the signs of the number Pi, there is no end and the possibilities of the practical application of this useful, elusive number of pi.
In modern mathematics, the number of pi is not only the ratio of the length of the circumference to the diameter, it enters big number various formulas.
This and other interdependes allowed the mathematicians to find out the nature of the pi.
The exact value of the number π in modern world It is not only its own scientific value, but also used for very accurate calculations (for example, satellite orbits, the construction of giant bridges), as well as assessing the speed and power of modern computers.
Currently, with the number π, a difficult-scale set of formulas, mathematical and physical facts is connected. Their number continues to grow rapidly. All this speaks of increasing interest in the most important mathematical constant, the study of which has more than twenty-two centuries.
I was interested in the work. I wanted to know about the history of the number π, practical application And I think that reached the goal. Summing up the work, I come to the conclusion that this topic is relevant. With the number π, many interesting facts are associated, so it causes interest in learning. In his work, I became interested in a detailed one - one of eternal valueswhich humanity has been using many centuries. I learned some aspects of his richest history. Found out why ancient world did not know the right circumstance length ratio to the diameter. I looked clearly, in what ways you can get a number. Based on experiments, calculated the approximate value of the number different ways. Conducted processing and analysis of the results of the experiment.
Any schoolboy today should know what is indicating and what is approximately equal to the number. After all, everyone has the first acquaintance with a number, using it when calculating the length of the circle, the area of \u200b\u200bthe circle occurs in 6th grade. But, unfortunately, these knowledge remain for many formal and after a year - two few people remember not only that the ratio of the circumference length to its diameter is the same for all circles, but even difficulty recall the number of numbers equal to 3 ,fourteen.
I tried to raise the curtain of the richest history of the number that humanity has been using many centuries. He independently made a presentation to his work.
The history of numbers is fascinating and mysterious. I would like to continue the study of other amazing numbers in mathematics. This will become the object of my next research studies.
Bibliography.
1. Glaser G.I. The history of mathematics at school IV- VI classes. - M.: Enlightenment, 1982.
2. Depman I.Ya., Vilenkin N.Ya. Behind the pages of the textbook of mathematics - M.: Enlightenment, 1989.
3. Zhukov A.V.Thestressive number "PI". - M.: UrSS Editorial, 2004.
4. Kympan F. History of the number "PI". - M.: Science, 1971.
5. Sandles A.A. Journey to the history of mathematics - M.: Pedagogy - Press, 1995.
6. Encyclopedia for children. T.11. Mathematics - M.: Avanta +, 1998.
Internet resources:
- http: // crow.academy.ru/ materials_ / pi / history.htm
Http: //hab/kp.ru// Daily / 24123/344634 /
Today is the birthday of the number of Pi, who, on the initiative of American mathematicians, is celebrated on March 14 at 1 o'clock and 59 minutes of afternoon. This is due to the more accurate value of the PI number: we all accustomed to consider this constant as 3.14, but the number can be continued as follows: 3, 14159 ... Transferring it to the 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 "Day of Pi" should still be considered July 22, because in the European dates format this day is recorded 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 the circumference to the diameter of the circle, goes into distant antiquity," says the shoal. - Already, Sumerians and Babylonians knew that this this attitude does not depend on the diameter of the circle and is constant. One of the first references to the number Pi can be found in the texts egyptian scribe Akhmesa (about 1650 BC. e.). Ancient Greeks, many borrowed from the Egyptians, contributed to the development of this mysterious value. According to the legend, Archimedesit was so passionate about the calculations that he did not notice how Roman soldiers took his native city of Syracuse. When the Roman soldier approached him, Archimedes shouted in Greek: "Do not touch my circles!". In response, the soldier is broken with his sword.
Platoreceived the rather accurate value of the PI number for its time - 3,146. Ludolf baths Zeileni spent most of my life above the calculations of the first 36 digits after the semicolons of the pi number, and they were engraved on his tombstone after death. "
Irrational and abnormal
According to the professor, at all times the pursuit of the calculation of new decimal signs was determined by the desire to obtain the exact meaning of this number. It was assumed that the number Pi is rational and, therefore, can be expressed by a simple fraction. And this is rooted incorrectly!
The number Pi is also more because it is a mystical. Since ancient times, a religion of the confent holders existed. In addition to the traditional value of Pi - the mathematical constant (3,1415 ...), expressing the ratio of the circumference of it to its diameter, there is a mass of other values \u200b\u200bof the number. Curious facts are curious. In the process of measurements of the size of the Great Pyramid in Giza, it turned out that it has the same ratio of height to the perimeter of its base, as a radius of the circle to its length, that is, ½ pi.
If you calculate the length of the Earth's equator using the Pi number with an accuracy of the ninth sign, the error in calculations will be only about 6 mm. Thirty nine marks after a semicolons Among the pi is enough to calculate the length of the circle, hailing known space objects In the universe, with an error is not greater than the radius of the hydrogen atom!
The study of PI is involved in the mathematical analysis. Photo: AIF / Nadezhda Uvarova
Chaos in numbers
According to Professor of Mathematics, in 1767 Lamberti installed the irrationality of the number Pi, that is, the inability to present it with the attitude of two integers. This means that the sequence of decimal signs of the pi is chaos, emitted in numbers. In other words, in the "tail" of decimal signs contain any number, any sequence of numbers, any texts that were, there are and will be, but only to extract this information is not possible!
"The exact value of the number of PI is impossible to find out - Vladimir Ilyich continues. - But these attempts are not left. In 1991. Musicovsky A new constant signs have achieved, and in 1994 - 4044000000. After that, the number of faithful signs of the number pi increased avalanche-like ".
World record for memorizing the number of pi among the Chinese Liu Chao.Who managed to remember 67890 decimal places without error and reproduce them within 24 hours and 4 minutes.
About "golden section"
By the way, the relationship between PI and another amazing value - the golden cross section is actually never proven. People have long noticed that the "golden" proportion is the same number f - and the number of Pi, divided into two, differ in less than 3% (1.61803398 ... and 1,57079632 ...). However, for mathematics, these three percent - the difference is too significant to consider these values \u200b\u200bidentical. In the same way, it can be said that the PI number and the number of fi are relatives of another known constant - the number of Euler, as the root of it is close to half of the number Pi. One second pi - 1, 5708, fi - 1,6180, root of e - 1, 6487.
This is only part of the pi value. Photo: Screenshot
Birthday Py.
In South Ural state University Birthday constants celebrate all teachers and mathematics students. So it was always - it is impossible to say that interest appeared only in last years. The number 3.14 greets even a special festive concert!
For many centuries, and even, oddly enough, millennia, people understand the importance and value for science of a mathematical constant equal to the ratio of the circumference of the circumference to its diameter. the number of pi is still unknown, but the most the best mathematicians Throughout our history. Most of them wanted to express it to a rational number.
1. Researchers and true fans of PI numbers organized a club for entry into which you need to know by heart a large number of His signs.
2. Since 1988, the "Day of the PI" day is celebrated, which falls on March 14. Prepare salads, cakes, cookies, cakes with his image.
3. The number of PI has already shifted to music, while it sounds quite well. He even erected a monument in American Seattle in front of the building of the city museum of arts.
At that distant time, the PI number tried to calculate with the help of geometry. The fact that this number is constantly for a variety of circles, they knew still geometers in ancient Egypt, Babylon, India and Ancient Greecewho affirmed in their works that it is just a little more than three.
In one of the sacred books of Jainism (an ancient Indian religion, which arose in the VI century. BC) it is mentioned that then the number Pi was considered equal to the root square of ten, which in the end gives 3,162 ....
The ancient Greek mathematicians were measured by the circumference by the method of building a segment, but in order to measure the circle, they had to build an equilibrium square, that is, a figure equal to it in the area.
When not yet knew decimal fractions, The Great Archimeda found the value of the number Pi with an accuracy of 99.9%. He opened the way that became the basis of many subsequent calculations, entered the circle and described it around it right polygons. As a result, Archimeda calculated the value of the number Pi as ratio 22/7 ≈ 3,142857142857143.
In China, Mathematics and Court Astronomer, Czu Chunchi in the V century BC. e. Denotes a more accurate value of the number of PI, having calculated it to seven digits after the comma and determined its value between the numbers 3, 1415926 and 3,1415927. More than 900 years needed scientists to continue this digital series.
Middle Ages
Famous Indian scientist Madhava, who lived at the turn of the XIV - XV centuries, who became the founder of the Kerala school of astronomy and mathematics, for the first time in history began to work on decomposition trigonometric functions in the ranks. True, only two of his work remained, and only links and quotes of his students are known to others. In the scientific treaty "Mahajianna", which is attributed to Madhava, it is indicated that the number Pi is equal to 3,14159265359. And in the Sadratamala treatise, a number with an even large number of accurate decimal places is given: 3,14159265358979324. In these numbers, the latest numbers do not correspond to the correct value.
In the XV century, the Samarkand mathematician and astronomer Al-Kashi calculated the number of pi with sixteen decimal signs. Its result was considered the most accurate over the next 250 years.
W. Johnson, a mathematician from England, one of the first could designate the ratio of the circumference length to its diameter of the letter π. Pi is the first letter of the Greek word "περιφέέεια" - a circle. But this designation was able to become generally accepted only after they took advantage of the more famous scientist L. Eyler in 1736.
Conclusion
Modern scientists continue to work on further calculations of the values \u200b\u200bof the PI number. Supercomputers are already used for this. In 2011, a scholar from Cigar Condo, cooperating with American student Alexander Yi, made a correct calculation of the sequence of 10 trillion digits. But still it is not clear who discovered the number of Pi, who first thought about this problem and produced the first calculations of this, a truly mystical number.
They mentioned about the question "What would happen to the world if the number pi was 4?" I decided to reflect on this topic slightly using some (albeit not the most extensive) knowledge in the respective areas of mathematics. Who is interested - I ask for Cat.
To present such a world, you need to mathematically realize the space with a different ratio of the circumference length to its diameter. That I tried to do.
Attempt number 1.
We will discuss right away that I will only consider two-dimensional spaces. Why? Because the circle itself is defined in a two-dimensional space (if you consider the dimension n\u003e 2, the ratio of the measure (N-1) of the dimensional circle to its radius will not even be a constant).So first, I tried to come up with at least some space where Pi is not equal to 3.1415 ... For this, I took a metric space with a metric, in which the distance between two points is equal to the maximum among coordinate difference modules (i.e. Chebyshev distance).
What kind will there be a single circle in this space? Take a point with coordinates (0.0) for the center of this circle. Then the set of points, the distance (in the sense of a given metric) from which to the center is equal to 1, there are 4 segments parallel to the axes of coordinates forming the square with a side 2 and the center in zero.
Yes, in some metric it is a circle!
Consider here Pi. The radius is 1, then the diameter, respectively, is 2. You can also consider the definition of the diameter as the greatest distance between two points, but even so it is equal to 2. It remains to find the length of our "circle" in this metric. This is the sum of the lengths of all four segments, which in this metric have the length of MAX (0.2) \u003d 2. So, the length of the circle is 4 * 2 \u003d 8. Well, then Pi here is 8/2 \u003d 4. Happened! But do you need to rejoice hard? This result is practically useless, because the space under consideration is absolutely abstract, it is not even defined angles and turns. You can imagine the world where the turn is not defined, and where is the circle of the square? I tried to be honest, but I did not have enough imagination.
Radius is 1, but with the length of the length of this "circle" there are some difficulties. After some search information on the Internet, I came to the conclusion that in the pseudo-chilide space such a concept as the "PI number" can not be determined at all, which is definitely bad.
If someone in the comments tell me how to formally consider the length of the curve in the pseudo-chilide space, I will be very happy, because my knowledge in differential geometry, topology (as well as zealous google) was not enough for this.
Conclusions:
I do not know if it is possible to write about the conclusions after such not very long research, but you can say something. First, trying to present space with a different number of pi, I realized that it would be too abstract to be a real-world model. Secondly, when if you try to come up with a more successful model (similar to ours, real world), it turns out that the number PI will remain unchanged. If you make a negative square of the distance (which for ordinary person - Just absurd), then pi will not be determined at all! All this suggests that, perhaps, the world with another number of Pi and could not be at all? After all, it is not for nothing that the universe is exactly what it is. Or maybe it is real, only ordinary mathematics, physics and human imagination for this is not enough. What do you think?UPD. I learned exactly. The length of the curve in the pseudo-chilide space can be determined only on any of its Euclidean subspace. That is, in particular, for the "circle" in an attempt, such a concept as "Length" is not determined at all. Accordingly, Pi there is also impossible.
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