1. The history of number has more than one millennium, almost as long as the science of mathematics exists. Of course, the exact value of the number was not immediately calculated. At first, 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.
2. In different eras and different peoples Pi has different meanings. For example, in ancient Egypt it was 3.1604, among the Hindus it acquired the value of 3.162, the Chinese used the number equal to 3.1459. Over time, π was calculated more and more accurately, and when computer technology appeared, that is, a computer, it began to have more than 4 billion characters.
3. Mathematicians around the world do not stop doing research related to the number Pi. It is literally shrouded in mystery. Some theorists even believe that it contains a universal truth. In order to share knowledge and new information about Pi, they organized the Pi Club. Entering it is not easy, you need to have an outstanding memory. So, those wishing to become a member of the club are examined: a person must tell as many signs of the number Pi from memory as possible.
4. They even came up with various techniques for remembering the number 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 digit after the decimal point. To further simplify the memorization of such a long number, they compose verses according to the same principle.
Members of the Pi Club 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 in which each word was equal to almost four thousand (3834) first digits of pi.
5. There are even people who have set records for memorizing Pi signs. So, in Japan, Akira Haraguchi memorized more than eighty-three thousand characters. But the domestic 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.
6. 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 in the celebration of Pi Day.
7. Interestingly, the pyramid of Cheops is a kind of embodiment of the number Pi in nature, the ratio between the height and the perimeter of the base results in the number 3.14.
8. There is a Pi language. Fascinated by literature, mathematicians invented a dialect in which the number of letters in all words corresponds to the numbers Pi in exact order. Writer Mike Keith even wrote a book, Not a Wake, which is completely written in the Pi language.
Practical part
An experiment to calculate the approximate value of the ratio of the circumference to the diameter.
Take any 5 items: a tennis ball, a glass, a mug, a jar, a jar for tennis balls.
We measure the diameter of each object and the circumference using a thread and a ruler with a division value of 1 mm and, accordingly, an error of 0.5 mm.
Let us calculate for each case the value of the number " Pi”, rounding the result to thousandths.
Conclusion: the ratio of circumference to diameter approaches 3.14. The accuracy of calculating the number " Pi» in this way is small: only in one case out of 5 the found value of the constant contains the correct digit in the hundredth place, in other cases the accuracy is achieved only in the tenth place.
Conclusion
The PI number appears in formulas used in many fields. Physics, electrical engineering, electronics, probability theory, construction and navigation are just some of them. And it seems that just as there is no end to the signs of the number PI, so there is no end to the possibilities practical application this useful, elusive number of PIs.
In modern mathematics, the number pi is not only the ratio of the circumference of a circle to its diameter, it is included in big number various formulas. This and other interdependencies allowed mathematicians to further understand the nature of the number pi.
Literature
- Zhukov A.V. The ubiquitous Pi. – Editorial URSS, 2004. Zhukov A. V. On the number π. - Editorial URSS, 2004.
- Wikipedia
- Website: -Club or Number Fanatics Club
- ME AND. Perelman " Interesting geometry". - M.: AST.Astrel, 2003. Emotional presentation of the children of incommensurability. // Mathematics at school - 1998 - No. 1 - p. 76-77.
- Pi is a magical geometric symbol. // Mathematics - 1993 - No. 27 - 28.
What is the number pi we know and remember from school. It is equal to 3.1415926 and so on... It is enough for an ordinary person to know that this number is obtained by dividing the circumference of a circle by its diameter. But many people know that the number Pi appears in unexpected areas not only in mathematics and geometry, but also in physics. Well, if you delve into the details of the nature of this number, you can see a lot of surprises among the endless series of numbers. Is it possible that Pi hides the deepest secrets of the universe?
Infinite number
The number Pi itself arises in our world as the length of a circle, the diameter of which is equal to one. But, despite the fact that the segment equal to Pi is quite finite, the number Pi starts like 3.1415926 and goes to infinity in rows of numbers that never repeat. The first surprising fact is that this number, used in geometry, cannot be expressed as a fraction of whole numbers. In other words, you cannot write it as a ratio of two numbers a/b. In addition, the number Pi is transcendental. This means that there is no such equation (polynomial) with integer coefficients, the solution of which would be Pi.
The fact that the number Pi is transcendent was proved in 1882 by the German mathematician von Lindemann. It was this proof that became the answer to the question whether it is possible to draw a square with a compass and a ruler, whose area is equal to the area of a given circle. This problem is known as the search for the squaring of a circle, which has troubled mankind since ancient times. It seemed that this problem had a simple solution and was about to be revealed. But it was an incomprehensible property of pi that showed that the problem of squaring a circle has no solution.
For at least four and a half millennia, mankind has been trying to get an increasingly accurate value of pi. For example, in the Bible in the 1st Book of Kings (7:23), the number pi is taken equal to 3.
Remarkable in accuracy, the value of Pi can be found in the pyramids of Giza: the ratio of the perimeter and height of the pyramids is 22/7. This fraction gives an approximate value of Pi, equal to 3.142 ... Unless, of course, the Egyptians set such a ratio by accident. The same value already in relation to the calculation of the number Pi was received in the III century BC by the great Archimedes.
In the Ahmes Papyrus, an ancient Egyptian mathematics textbook that dates back to 1650 BC, Pi is calculated as 3.160493827.
In ancient Indian texts around the 9th century BC, the most accurate value was expressed by the number 339/108, which equaled 3.1388 ...
For almost two thousand years after Archimedes, people have been trying to find ways to calculate pi. Among them were both famous and unknown mathematicians. For example, the Roman architect Mark Vitruvius Pollio, the Egyptian astronomer Claudius Ptolemy, the Chinese mathematician Liu Hui, the Indian sage Ariabhata, the medieval mathematician Leonardo of Pisa, known as Fibonacci, the Arab scientist Al-Khwarizmi, from whose name the word "algorithm" appeared. All of them and many other people were looking for the most accurate methods for calculating Pi, but until the 15th century they never received more than 10 digits after the decimal point due to the complexity of the calculations.
Finally, in 1400, the Indian mathematician Madhava from the Sangamagram calculated Pi with an accuracy of up to 13 digits (although he still made a mistake in the last two).
Number of signs
In the 17th century, Leibniz and Newton discovered the analysis of infinitesimal quantities, which made it possible to calculate pi more progressively - through power series and integrals. Newton himself calculated 16 decimal places, but did not mention this in his books - this became known after his death. Newton claimed that he only calculated Pi out of boredom.
At about the same time, other lesser-known mathematicians also pulled themselves up, proposing new formulas for calculating the number Pi through trigonometric functions.
For example, here is the formula used to calculate Pi by astronomy teacher John Machin in 1706: PI / 4 = 4arctg(1/5) - arctg(1/239). Using methods of analysis, Machin derived from this formula the number Pi with a hundred decimal places.
By the way, in the same 1706, the number Pi received an official designation in the form of a Greek letter: William Jones used it in his work on mathematics, taking the first letter of the Greek word “periphery”, which means “circle”. Born in 1707, the great Leonard Euler popularized this designation, now known to any schoolchild.
Before the era of computers, mathematicians were concerned with calculating as many signs as possible. In this regard, sometimes there were curiosities. Amateur mathematician W. Shanks calculated 707 digits of pi in 1875. These seven hundred signs were immortalized on the wall of the Palais des Discoveries in Paris in 1937. However, nine years later, observant mathematicians found that only the first 527 characters were correctly calculated. The museum had to incur decent expenses to correct the mistake - now all the numbers are correct.
When computers appeared, the number of digits of Pi began to be calculated in completely unimaginable orders.
One of the first electronic computers ENIAC, created in 1946, which was huge and generated so much heat that the room warmed up to 50 degrees Celsius, calculated the first 2037 digits of pi. This calculation took the car 70 hours.
As computers improved, our knowledge of pi went further and further into infinity. In 1958, 10 thousand digits of the number were calculated. In 1987, the Japanese calculated 10,013,395 characters. In 2011, Japanese researcher Shigeru Hondo passed the 10 trillion mark.
Where else can you find Pi?
So, often our knowledge of the number Pi remains at the school level, and we know for sure that this number is indispensable in the first place in geometry.
In addition to the formulas for the length and area of a circle, the number Pi is used in the formulas for ellipses, spheres, cones, cylinders, ellipsoids, and so on: somewhere the formulas are simple and easy to remember, and somewhere they contain very complex integrals.
Then we can meet the number pi in mathematical formulas, where, at first glance, geometry is not visible. For example, indefinite integral from 1/(1-x^2) is equal to Pi.
Pi is often used in series analysis. For example, here is a simple series that converges to pi:
1/1 - 1/3 + 1/5 - 1/7 + 1/9 - .... = PI/4
Among series, pi appears most unexpectedly in the well-known Riemann zeta function. It will not be possible to tell about it in a nutshell, we will only say that someday the number Pi will help to find a formula for calculating prime numbers.
And it is absolutely amazing: Pi appears in two of the most beautiful "royal" formulas of mathematics - the Stirling formula (which helps to find the approximate value of the factorial and the gamma function) and the Euler formula (which relates as many as five mathematical constants).
However, the most unexpected discovery awaited mathematicians in probability theory. Pi is also there.
For example, the probability that two numbers are relatively prime is 6/PI^2.
Pi appears in Buffon's 18th-century needle-throwing problem: what is the probability that a needle thrown onto a sheet of paper with a pattern will cross one of the lines. If the length of the needle is L, and the distance between the lines is L, and r > L, then we can approximately calculate the value of Pi using the probability formula 2L/rPI. Just imagine - we can get Pi from random events. And by the way Pi is present in the normal probability distribution, appears in the equation of the famous Gaussian curve. Does this mean that pi is even more fundamental than just the ratio of a circle's circumference to its diameter?
We can meet Pi in physics as well. Pi appears in Coulomb's law, which describes the force of interaction between two charges, in Kepler's third law, which shows the period of revolution of a planet around the Sun, and even occurs in the arrangement of electron orbitals of a hydrogen atom. And, again, the most incredible thing is that the Pi number is hidden in the formula of the Heisenberg uncertainty principle, the fundamental law of quantum physics.
Secrets of Pi
In Carl Sagan's novel "Contact", which is based on the film of the same name, aliens inform the heroine that among the signs of Pi there is a secret message from God. From a certain position, the numbers in the number cease to be random and represent a code in which all the secrets of the Universe are recorded.
This novel actually reflected the riddle that occupies the minds of mathematicians all over the planet: is the number Pi a normal number in which the digits are scattered with the same frequency, or is there something wrong with this number. And although scientists tend to the first option (but cannot prove it), Pi looks very mysterious. A Japanese man once calculated how many times the numbers from 0 to 9 occur in the first trillion digits of pi. And I saw that the numbers 2, 4 and 8 are more common than the rest. This may be one of the hints that Pi is not quite normal, and the numbers in it are really not random.
Let's remember everything that we have read above and ask ourselves, what other irrational and transcendental number is so common in the real world?
And there are other oddities in store. For example, the sum of the first twenty digits of Pi is 20, and the sum of the first 144 digits is equal to the "number of the beast" 666.
The protagonist of the American TV series The Suspect, Professor Finch, told students that, due to the infinity of the number pi, any combination of numbers can occur in it, from the numbers of your date of birth to more complex numbers. For example, in the 762nd position there is a sequence of six nines. This position is called the Feynman point, after the famous physicist who noticed this interesting combination.
We also know that the number Pi contains the sequence 0123456789, but it is located on the 17387594880th digit.
All this means that in the infinity of the Pi number one can find not only interesting combinations of numbers, but also the encoded text of "War and Peace", the Bible and even the Main Secret of the Universe, if it exists.
By the way, about the Bible. The well-known popularizer of mathematics Martin Gardner in 1966 stated that the millionth sign of the number Pi (still unknown at that time) would be the number 5. He explained his calculations by the fact that in the English version of the Bible, in the 3rd book, 14th chapter, 16 -m verse (3-14-16) the seventh word contains five letters. The million figure was received eight years later. It was number five.
Is it worth it after this to assert that the number pi is random?
Mathematicians all over the world eat a piece of cake every year on March 14 - after all, this is the day of Pi, the most famous irrational number. This date is directly related to the number whose first digits are 3.14. Pi is the ratio of the circumference of a circle to its diameter. Since it is irrational, it is impossible to write it as a fraction. This is an infinitely long number. It was discovered thousands of years ago and has been constantly studied ever since, but does Pi have any secrets left? From ancient origins to an uncertain future, here are some of the most interesting facts about pi.
Memorizing Pi
The record for remembering numbers after the decimal point belongs to Rajveer Meena from India, who managed to remember 70,000 digits - he set the record on March 21, 2015. Before that, the record holder was Chao Lu from China, who managed to memorize 67,890 digits - this record was set in 2005. The unofficial record holder is Akira Haraguchi, who recorded on video his repetition of 100,000 digits in 2005 and recently published a video where he manages to remember 117,000 digits. An official record would only become if 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 memorize the number Pi. Many people use various mnemonic techniques, such as poetry, where the number of letters in each word is the same as pi. Each language has its own variants of such phrases, which help to remember both the first few digits and a whole hundred.
Pi language exists
Fascinated by literature, mathematicians invented a dialect in which the number of letters in all words corresponds to the digits of Pi in exact order. Writer Mike Keith even wrote a book, Not a Wake, which is completely written in the Pi language. Enthusiasts of such creativity write their works in full accordance with the number of letters and the meaning of the numbers. This has no practical application, but is a fairly common and well-known phenomenon in the circles of enthusiastic scientists.
Exponential Growth
Pi is an infinite number, so people, by definition, will never be able to determine the exact numbers of this number. However, the number of digits after the decimal point has increased greatly since the first use of the Pi. Even the Babylonians used it, but a fraction of three and one eighth was enough for them. Chinese and creators Old Testament and was completely limited to three. By 1665, Sir Isaac Newton had calculated 16 digits of pi. By 1719, French mathematician Tom Fante de Lagny had calculated 127 digits. The advent of computers has radically improved man's knowledge of Pi. From 1949 to 1967 the number known to man numbers skyrocketed from 2037 to 500,000. Not so long ago, Peter Trueb, a scientist from Switzerland, was able to calculate 2.24 trillion digits of Pi! This took 105 days. Of course, this is not the limit. It is likely that with the development of technology it will be possible to establish an even more accurate figure - since Pi is infinite, there is simply no limit to accuracy, and only the technical features of computer technology can limit it.
Calculating Pi by hand
If you want to find the number yourself, you can use the old fashioned technique - you will need a ruler, a jar and string, you can also use a protractor and a pencil. The downside to using a jar is that it has to be round, and accuracy will be determined by how well the person can wrap the rope around it. It is possible to draw a circle with a protractor, but this also requires skill and precision, as an uneven circle can seriously distort your measurements. A more accurate method involves the use of geometry. Divide the circle into many segments, like pizza slices, and then calculate the length of a straight line that would turn each segment into isosceles triangle. The sum of the sides will give an approximate number of pi. The more segments you use, the more accurate the number will be. Of course, in your calculations you will not be able to come close to the results of a computer, nevertheless, these simple experiments allow you to understand in more detail what Pi is in general and how it is used in mathematics. 
Discovery of Pi
The ancient Babylonians knew about the existence of the number Pi already four thousand years ago. The Babylonian tablets calculate Pi as 3.125, and the Egyptian mathematical papyrus contains the number 3.1605. In the Bible, the number Pi is given in an obsolete length - in cubits, and the Greek mathematician Archimedes used the Pythagorean theorem to describe Pi, the geometric ratio of the length of the sides of a triangle and the area of \u200b\u200bthe figures inside and outside the circles. Thus, it is safe to say that Pi is one of the most ancient mathematical concepts, although the exact name given number and appeared relatively recently.
A new take on Pi
Even before pi was related to circles, mathematicians already had many ways to even name this number. For example, in ancient mathematics textbooks one can find a phrase in Latin, which can be roughly translated as "the quantity that shows the length when the diameter is multiplied by it." The irrational number became famous when the Swiss scientist Leonhard Euler used it in his work on trigonometry in 1737. However, the Greek symbol for pi was still not used - it only happened in a book by the lesser-known mathematician William Jones. He used it as early as 1706, but it was long neglected. Over time, scientists adopted this name, and now this is the most famous version of the name, although before it was also called the Ludolf number.
Is pi normal?
The number pi is definitely strange, but how does it obey the normal mathematical laws? Scientists have already solved many questions related to this irrational number but some mysteries remain. For example, it is not known how often all digits are used - the numbers from 0 to 9 should be used in equal proportion. However, statistics can be traced for the first trillion digits, but due to the fact that the number is infinite, it is impossible to prove anything for sure. There are other problems that still elude scientists. It is possible that the further development of science will help shed light on them, but on this moment it remains outside the human intellect.
Pi sounds divine
Scientists cannot answer some questions about the number Pi, however, every year they understand its essence better. Already in the eighteenth century, the irrationality of this number was proved. In addition, it has been proved that the number is transcendental. This means that there is no definite formula that would allow you to calculate pi using rational numbers. 
Dissatisfaction with Pi
Many mathematicians are simply in love with Pi, but there are those who believe that these numbers have no special significance. In addition, they claim that the number Tau, which is twice the size of Pi, is more convenient to use as an irrational one. Tau shows the relationship between the circumference and the radius, which, according to some, represents a more logical method of calculation. However, it is impossible to unambiguously determine anything in this matter, and one and the other number will always have supporters, both methods have the right to life, so this is just an interesting fact, and not a reason to think that you should not use the number Pi.
There are an infinite number of different numbers in mathematics. Most of them do not attract attention at all. However, some, at first glance, absolutely uninteresting numbers are so well known that they even have their own names. One of these constants is the irrational number Pi, which was studied at school and used to calculate the area or perimeter of a circle along a given radius.
From the history of the constant
Interesting Facts about the number Pi - the history of the study. The existence of a constant counts about 4 millennia. In other words, it is a little younger than the science of mathematics itself.
The first evidence that the number pi was known in ancient Egypt is in the papyrus of Ahmes, one of the oldest problem books found. The document dates from approximately 1650 BC. e. In papyrus, the constant was assumed to be 3.1605. This is a fairly accurate value, given that other peoples used 3 to calculate the circumference of a circle from its diameter.
A little more accurately, the number Pi was calculated by Archimedes, the ancient Greek mathematician. He managed to approximate the value in the form of ordinary fractions 22/7 and 223/71. There is a legend that he was so busy calculating the constant that he did not pay attention to how the Romans captured his city. At that moment, when the warrior approached the scientist, Archimedes shouted to him not to touch his drawings. These words of the mathematician were the last.
Al-Khwarizmi, the founder of algebra, who lived in the 8th-9th centuries, worked on the calculations of the constant. With a small error, he received the number Pi, equal to 3.1416.
After 8 centuries, the mathematician Ludolf van Zeulen correctly identified 36 decimal places. For this achievement, the Pi number is sometimes called the Ludolf constant (other well-known names are the Archimedean constant or the circular constant), and the figures obtained by the scientist were engraved on his tombstone.
Around the same time, the constant began to be used not only for a circle, but also for calculating complex curves - arches and hypocycloids.
Only in early XVIII century, the constant began to be called the number Pi. The designation in the form of the letter π was not chosen by chance - it is with it that 2 Greek words begin, meaning circle and perimeter. The name was proposed by the scientist Jones in 1706, and already 30 years later the image of this Greek letter is firmly used among other mathematical notations.
In the 19th century, William Shanks worked on calculating the first 707 characters of a constant. He failed to fully achieve the task - an error crept into the calculations, and the 527 figure turned out to be incorrect. However, even the result obtained was a good achievement for the science of that time.
AT late XIX century, the incorrect value of 3.2 was almost accepted at the state level in the state of Indiana. Fortunately, mathematicians managed to oppose the bill and prevent the error.
In the XX-XXI centuries. with the use of computer technology, the accuracy and speed of calculating the constant has increased thousands of times. By 2002, more than 1 trillion digits of the constant had been determined by computer in Japan. After 9 years, the accuracy of the calculation was already 10 trillion characters after the decimal point.
In art and marketing
Even though Pi is a mathematical constant, over the years people have tried to use the irrational and mysterious value in other areas of life, including in works of art.
The very first signs of a constant were found in a monument of architecture in Giza. When determining the size of the Great Pyramid, it turned out that the ratio of the perimeter of its base to the height is π. It is only unknown whether the architect wanted to use his knowledge of this number, or whether such a ratio came out by accident.
Currently, the number Pi is also not deprived of attention in creativity. For example, if you mark each note of the minor scale with a number from 0 to 9, and then play the resulting sequence in the form of pi on a musical instrument, you can enjoy an unusual melody with an interesting sound.
Constant also did not bypass the cinema. The drama film Pi: Faith in Chaos won Best Director at the Sundance Film Festival. According to the plot main character is in search of simple and understandable answers to questions about the constant, which as a result almost drove him crazy. References to the number are also found in other movies and TV shows.
The number has found its application even in such an unexpected area as marketing. So, the Givenchy company produced a cologne called "Pi".
Constant and society
Some features of the number:
- The constant is an irrational value. This means that it cannot be represented as a ratio of two numbers. In addition, there is no regularity in his record.
- Characters repeating in a row in a constant are not uncommon. So, for every 20-30 characters, there are usually at least 2 consecutive numbers. Sequences of 3 characters are already rarer, they come across with a frequency of about 1 repetition per 150-300 characters. And on the 763rd sign, a chain of 6 consecutive nines begins. This place in the record even has its own name - the Feynman point.
- If we consider the first million characters, then according to statistics, the rarest numbers in it will be 6 and 1, and the most frequent - 5 and 4.
- The number 0 appears in the sequence later than the rest, only on 31 characters.
- In trigonometry, a 360 degree angle and a constant are closely related. Oddly enough, but at 358, 359 and 360 positions after the decimal point is the number 360.
In order to exchange information about discoveries, the Pi Club was established. Those wishing to join it have to pass a difficult test: a future member of the mathematical community must correctly name as many signs of the constant as possible from memory.
Of course, memorizing a long numerical sequence that does not have patterns and repetitions is a rather difficult task. To facilitate the task, various texts and poems are invented in which the number of letters in a word corresponds to a certain figure of the constant. This method of memorization is popular with members of the Pi Club. One of the longest stories contained 3834 first digits of the number.
Monument at the Museum of Art in Seattle
However, the recognized champions in memorization are, of course, the inhabitants of China and Japan. So, the Japanese Akira Haraguchi was able to learn over 83 thousand digits after the decimal point. And the Chinese Liu Chao became famous as a man who was able to name 67,890 symbols of the number Pi in a record time of 24 hours. Wherein average speed was 47 characters in 1 minute. Initially, his goal was to name 93 thousand numbers, but he made a mistake, after which he did not continue.
To emphasize the meaning of the constant, a monument in the form of a huge Greek letter π was erected in front of the Museum of Art in Seattle.
In addition, Pi Day has been celebrated every March 14 since 1988. The date coincides with the first signs of the constant - 3.14. Celebrate it after 1:59. On this day, interested people treat themselves to cakes and cookies with the Pi symbol, after which various mathematical contests and quizzes are held. By the way, A. Einstein, astronomer Schiaparelli and cosmonaut Cernan were born on this day.
The Pi number is an amazing constant that has found its application in a variety of fields, from technology and construction to the arts. Like any other value that is used frequently and which cannot be fully calculated, it will always attract the attention of mathematicians, physicists and other scientists.
Interesting facts about the Number PI
"PI" is the most used mathematical constant in the world. In the twentieth century Pi" has been used in many fields such as number theory, probability, and chaos theory.
"PI" is an irrational number, that is, it has no finite value.
In 1995, Hiroyoki Gtou memorized 42,195 decimal places of PI and is considered the reigning PI champion.
Rudolf van Selen (1540-1610) calculated the first 36 digits of the number "PI". According to legend, these figures were engraved on his tombstone.
William Shanks (1812-1882) worked on calculating the first 707 digits of the number "PI". Unfortunately, he made a mistake after the 527th, and the following numbers were not correct.
In 2002, a Japanese scientist calculated 1,240,000 million digits of the number "PI" using a powerful computer, breaking all previous records.
By 2000 BC, the Babylonians had calculated a constant for the ratio of radius to circumference - 3-1/8 or 3.125. The ancient Egyptians found a slightly different ratio - 3-1/7 or 3.143.
Pi Day is celebrated on March 14 (which was chosen because it resembles 3.14). The official celebration begins at 1:59 a.m. to match the number 3.14159 with the date.
William Jones (1675-1749) introduced the "PI" symbol in 1706.
In September 2010, Nicholas Zhe of technology company Yahoo was able to identify 2,000,000,000,000,000 digits of Pi after the decimal point - two quadrillion digits. If this work were carried out on a single computer, it would require more than 500 years. But Zhe used the technology of the so-called cloud computing "Hadoop" - a "cloud" of thousands of computers was involved at the same time. And even so, it took 23 days as a calculation.
The symbol "Pi" (π) has been used in mathematical formulas for over 250 years.
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, 1/2π.
The first 144 digits after the decimal point of Pi end in 666, which is referred to in the Bible as the "number of the beast".
The first one million decimal places in Pi consists of: 99959 zeros, 99758 ones, 100026 twos, 100229 triplets, 100230 fours, 100359 fives, 99548 sixes, 99800 sevens, 99985 eights and 100106 nines.
What is Pi hiding?
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 searched for and found in sacred texts. 1 Who discovered π? 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.
In ancient Egypt, pi was 3.16.
AT 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 a circle, that is, the impossibility of constructing a square with a compass and a 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. Should have written twice. odd numbers: 11 33 55, and then, dividing them in half, place 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.
The number acquired its designation π in a complicated way: at first, the mathematician Outrade called the circumference with this Greek letter in 1647. 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.
How to remember the number Pi
For memorization, you can use the following memos. To restore the number, you need to count the number of characters in each of the words and write it down in order.
- So that we don't make mistakes
It needs to be read correctly:
ninety two and six - You just have to try
And remember everything as it is:
Three, fourteen, fifteen
Ninety-two and six. - Three, fourteen, fifteen, nine two, six five, three five
Eight nine, seven and nine, three two, three eight, forty six
Two six four, three three eight, three two seven nine, five zero two
Eight eight and four nineteen seven one