(), and it became generally accepted after the work of Euler. This designation comes from the initial letter of the Greek words περιφέρεια - circle, periphery and περίμετρος - perimeter.
Ratings
- 510 decimal places: π ≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930 381 964 428 810 975 665 933 446 128 475 648 233 786 783 165 271 201 909 145 648 566 923 460 348 610 454 326 648 213 393 607 260 249 141 273 724 587 006 606 315 588 174 881 520 920 962 829 254 091 715 364 367 892 590 360 011 330 530 548 820 466 521 384 146 951 941 511 609 433 057 270 365 759 591 953 092 186 117 381 932 611 793 105 118 548 074 462 379 962 749 567 351 885 752 724 891 227 938 183 011 949 129 833 673 362…
Properties
Ratios
There are many known formulas with the number π:
- Wallis formula:
- Euler's identity:
- T.n. "Poisson integral" or "Gauss integral"
Transcendence and irrationality
Unsolved problems
- It is not known whether the numbers π and e algebraically independent.
- It is unknown whether the numbers π + e , π − e , π e , π / e , π e , π π , e e transcendental.
- Until now, nothing is known about the normality of the number π; it is not even known which of the digits 0-9 appear in the decimal representation of the number π an infinite number of times.
Calculation history
and Chudnovsky
Mnemonic rules
So that we do not make mistakes, We must read correctly: Three, fourteen, fifteen, 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. To do science, everyone should know this. You can just try and repeat more often: “Three, fourteen, fifteen, Nine, twenty-six and five.”
2. Count the number of letters in each word in the phrases below ( excluding punctuation marks) and write down these numbers in a row - not forgetting about the decimal point after the first digit “3”, of course. The result will be an approximate number of Pi.
This I know and remember perfectly: But many signs are unnecessary for me, in vain.
Whoever, jokingly and soon, wishes Pi to know the number - already knows!
So Misha and Anyuta came running and wanted to find out the number.
(The second mnemonic is correct (with rounding of the last digit) only when using pre-reform spelling: when counting the number of letters in words, it is necessary to take into account hard signs!)
Another version of this mnemonic notation:
This I know and remember perfectly:
And many signs are unnecessary for me, in vain.
Let's trust our enormous knowledge
Those who counted the numbers of the armada.
If you follow the poetic meter, you can quickly remember:
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
Fun facts
Notes
See what “Pi” is in other dictionaries:
number- Receiving source: GOST 111 90: Sheet glass. Technical specifications original document See also related terms: 109. The number of betatron oscillations ... Dictionary-reference book of terms of normative and technical documentation
Noun, s., used. very often Morphology: (no) what? numbers, what? number, (see) what? number, what? number, about what? about number; pl. What? numbers, (no) what? numbers, why? numbers, (see) what? numbers, what? numbers, about what? about numbers mathematics 1. By number... ... Dictionary Dmitrieva
NUMBER, numbers, plural. numbers, numbers, numbers, cf. 1. The concept that serves as an expression of quantity, something with the help of which objects and phenomena are counted (mat.). Integer. A fractional number. Named number. Prime number. (see simple 1 in 1 value).… … Ushakov's Explanatory Dictionary
An abstract designation devoid of special content for any member of a certain series, in which this member is preceded or followed by some other specific member; abstract individual feature that distinguishes one set from... ... Philosophical Encyclopedia
Number- Number grammatical category, expressing quantitative characteristics objects of thought. Grammatical number is one of the manifestations of the more general linguistic category of quantity (see Language category) along with the lexical manifestation (“lexical... ... Linguistic encyclopedic dictionary
A number approximately equal to 2.718, which is often found in mathematics and natural sciences. For example, when a radioactive substance decays after time t, a fraction equal to e kt remains of the initial amount of the substance, where k is a number,... ... Collier's Encyclopedia
A; pl. numbers, sat, slam; Wed 1. A unit of account expressing a particular quantity. Fractional, integer, prime hours. Even, odd hours. Count in round numbers (approximately, counting in whole units or tens). Natural h. (positive integer... encyclopedic Dictionary
Wed. quantity, by count, to the question: how much? and the very sign expressing quantity, number. Without number; there is no number, without counting, many, many. Set up cutlery according to the number of guests. Roman, Arabic or church numbers. Integer, opposite. fraction... ... Dahl's Explanatory Dictionary
The ratio of the circumference of a circle to its diameter is the same for all circles. This ratio is usually denoted by the Greek letter (“pi” - the initial letter of the Greek word 
, which meant “circle”).
Archimedes, in his work “Measurement of a Circle,” calculated the ratio of the circumference to the diameter (number) and found that it was between 3 10/71 and 3 1/7.
For a long time, the number 22/7 was used as an approximate value, although already in the 5th century in China the approximation 355/113 = 3.1415929... was found, which was rediscovered in Europe only in the 16th century.
IN Ancient India considered equal to = 3.1622….
The French mathematician F. Viète calculated in 1579 with 9 digits.
The Dutch mathematician Ludolf Van Zeijlen in 1596 published the result of his ten-year work - the number calculated with 32 digits.
But all these clarifications of the value of the number were carried out using methods indicated by Archimedes: the circle was replaced by a polygon with all a large number sides The perimeter of the inscribed polygon was less than the circumference of the circle, and the perimeter of the circumscribed polygon was greater. But at the same time, it remained unclear whether the number was rational, that is, the ratio of two integers, or irrational.
Only in 1767 did the German mathematician I.G. Lambert proved that the number is irrational.
And more than a hundred years later, in 1882, another German mathematician, F. Lindemann, proved its transcendence, which meant the impossibility of constructing a square equal in size to a given circle using a compass and a ruler.
The simplest measurement
Draw a circle of diameter on thick cardboard d(=15 cm), cut out the resulting circle and wrap a thin thread around it. Measuring the length l(=46.5 cm) one full turn of the thread, divide l per diameter length d circles. The resulting quotient will be an approximate value of the number, i.e. = l/ d= 46.5 cm / 15 cm = 3.1. This rather crude method gives, under normal conditions, an approximate value of the number accurate to 1.
Measuring by weighing
Draw a square on a sheet of cardboard. Let's write a circle in it. Let's cut out a square. Let's determine the mass of a cardboard square using school scales. Let's cut a circle out of the square. Let's weigh him too. Knowing the masses of the square m sq. (=10 g) and the circle inscribed in it m cr (=7.8 g) let's use the formulas
where p and h– density and thickness of cardboard, respectively, S– area of the figure. Let's consider the equalities:
Naturally, in in this case the approximate value depends on the weighing accuracy. If the cardboard figures being weighed are quite large, then even on ordinary scales it is possible to obtain such mass values that will ensure the approximation of the number with an accuracy of 0.1.
Summing the areas of rectangles inscribed in a semicircle
Picture 1
Let A (a; 0), B (b; 0). Let us describe the semicircle on AB as a diameter. Divide the segment AB into n equal parts by points x 1, x 2, ..., x n-1 and restore perpendiculars from them to the intersection with the semicircle. The length of each such perpendicular is the value of the function f(x)=. From Figure 1 it is clear that the area S of a semicircle can be calculated using the formula
S = (b – a) ((f(x 0) + f(x 1) + … + f(x n-1)) / n.
In our case b=1, a=-1. Then = 2 S.
The more division points there are on segment AB, the more accurate the values will be. To facilitate monotonous computing work, a computer will help, for which program 1, compiled in BASIC, is given below.
Program 1REM "Pi Calculation"
REM "Rectangle Method"
INPUT "Enter the number of rectangles", n
dx = 1/n
FOR i = 0 TO n - 1
f = SQR(1 - x^2)
x = x + dx
a = a + f
NEXT i
p = 4 * dx * a
PRINT "The value of pi is ", p
END
The program was typed and launched with different parameter values n. The resulting number values are written in the table:
Monte Carlo method
This is actually a statistical testing method. It got its exotic name from the city of Monte Carlo in the Principality of Monaco, famous for its gambling houses. The fact is that the method requires the use of random numbers, and one of the simplest devices that generates random numbers is a roulette. However, you can get random numbers using...rain.
For the experiment, let's prepare a piece of cardboard, draw a square on it and inscribe a quarter of a circle in the square. If such a drawing is kept in the rain for some time, then traces of drops will remain on its surface. Let's count the number of tracks inside the square and inside the quarter circle. Obviously, their ratio will be approximately equal to the ratio of the areas of these figures, since drops will fall into different places in the drawing with equal probability. Let N cr– number of drops in a circle, N sq. is the number of drops squared, then
4 N cr / N sq.
Figure 2
Rain can be replaced with a table of random numbers, which is compiled using a computer using a special program. Let us assign two random numbers to each trace of a drop, characterizing its position along the axes Oh And OU. Random numbers can be selected from the table in any order, for example, in a row. Let the first four-digit number in the table 3265 . From it you can prepare a pair of numbers, each of which is greater than zero and less than one: x=0.32, y=0.65. We will consider these numbers to be the coordinates of the drop, i.e. the drop seems to have hit the point (0.32; 0.65). We do the same with all selected random numbers. If it turns out that for the point (x;y) If the inequality holds, then it lies outside the circle. If x + y = 1, then the point lies inside the circle.
To calculate the value, we again use formula (1). The calculation error using this method is usually proportional to , where D is a constant and N is the number of tests. In our case N = N sq. From this formula it is clear: in order to reduce the error by 10 times (in other words, to get another correct decimal place in the answer), you need to increase N, i.e. the amount of work, by 100 times. It is clear that the use of the Monte Carlo method was made possible only thanks to computers. Program 2 implements the described method on a computer.
Program 2REM "Pi Calculation"
REM "Monte Carlo Method"
INPUT "Enter the number of drops", n
m = 0
FOR i = 1 TO n
t = INT(RND(1) * 10000)
x = INT(t\100)
y = t - x * 100
IF x^2 + y^2< 10000 THEN m = m + 1
NEXT i
p=4*m/n
END
The program was typed and launched with different values of the parameter n. The resulting number values are written in the table:
| n | ||||||
| n | ||||||
Dropping needle method
Let's take an ordinary sewing needle and a sheet of paper. We will draw several parallel lines on the sheet so that the distances between them are equal and exceed the length of the needle. The drawing must be large enough so that an accidentally thrown needle does not fall outside its boundaries. Let us introduce the following notation: A- distance between lines, l– needle length.
Figure 3
The position of a needle randomly thrown onto the drawing (see Fig. 3) is determined by the distance X from its middle to the nearest straight line and the angle j that the needle makes with the perpendicular lowered from the middle of the needle to the nearest straight line (see Fig. 4). It's clear that
Figure 4
In Fig. 5 let's graphically represent the function y=0.5cos. All possible needle locations are characterized by points with coordinates (; y ), located on section ABCD. The shaded area of the AED is the points that correspond to the case where the needle intersects a straight line. Probability of event a– “the needle has crossed a straight line” – is calculated using the formula:
Figure 5
Probability p(a) can be approximately determined by repeatedly throwing the needle. Let the needle be thrown onto the drawing c once and p since it fell while crossing one of the straight lines, then with a sufficiently large c we have p(a) = p/c. From here = 2 l s / a k.
Comment. The presented method is a variation of the statistical test method. It is interesting from a didactic point of view, as it helps to combine simple experience with the creation of a rather complex mathematical model.
Calculation using Taylor series
Let us turn to the consideration of an arbitrary function f(x). Let us assume that for her at the point x 0 there are derivatives of all orders up to n th inclusive. Then for the function f(x) we can write the Taylor series:
Calculations using this series will be more accurate the more members of the series are involved. It is, of course, best to implement this method on a computer, for which you can use program 3.
Program 3REM "Pi Calculation"
REM "Taylor series expansion"
INPUT n
a = 1
FOR i = 1 TO n
d = 1 / (i + 2)
f = (-1)^i * d
a = a + f
NEXT i
p = 4 * a
PRINT "value of pi equals"; p
END
The program was typed and run with different values of the parameter n. The resulting number values are written in the table:
There are very simple mnemonic rules for remembering the meaning of a number: |
What is Pi equal to? we know and remember from school. It is equal to 3.1415926 and so on... To an ordinary person it is enough 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 of mathematics and geometry, but also in physics. Well, if you delve into the details of the nature of this number, you will notice many surprising things among the endless series of numbers. Is it possible that Pi is hiding the deepest secrets of the universe?
Infinite number
The number Pi itself appears in our world as the length of a circle whose diameter is equal to one. But, despite the fact that the segment equal to Pi is quite finite, the number Pi begins as 3.1415926 and goes to infinity in rows of numbers that are never repeated. First amazing 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 the ratio of two numbers a/b. In addition, the number Pi is transcendental. This means that there is no equation (polynomial) with integer coefficients whose solution would be the number Pi.
The fact that the number Pi is transcendental was proved in 1882 by the German mathematician von Lindemann. It was this proof that became the answer to the question of whether it is possible, using a compass and a ruler, to draw a square whose area is equal to the area of a given circle. This problem is known as the search for squaring a circle, which has worried humanity since ancient times. It seemed that this problem had a simple solution and was about to be solved. But it was precisely the incomprehensible property of the number Pi that showed that there was no solution to the problem of squaring the circle.
For at least four and a half millennia, humanity has been trying to obtain an increasingly accurate value for Pi. For example, in the Bible in the Third Book of Kings (7:23), the number Pi is taken to be 3.
The Pi value of remarkable accuracy can be found in the Giza pyramids: 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 this ratio by accident. The same value was already obtained in relation to the calculation of the number Pi in the 3rd century BC by the great Archimedes.
In the Papyrus of Ahmes, 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 was equal to 3.1388...
For almost two thousand years after Archimedes, people tried to find ways to calculate Pi. Among them were both famous and unknown mathematicians. For example, the Roman architect Marcus Vitruvius Pollio, the Egyptian astronomer Claudius Ptolemy, the Chinese mathematician Liu Hui, the Indian sage Aryabhata, 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 got more than 10 decimal places due to the complexity of the calculations.
Finally, in 1400, the Indian mathematician Madhava from Sangamagram calculated Pi with an accuracy of 13 digits (although he was still mistaken 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 it in his books - this became known after his death. Newton claimed that he calculated Pi purely out of boredom.
Around the same time, other lesser-known mathematicians also came forward and proposed new formulas for calculating the number Pi through trigonometric functions.
For example, this is the formula used to calculate Pi by astronomy teacher John Machin in 1706: PI / 4 = 4arctg(1/5) – arctg(1/239). Using analytical methods, Machin derived the number Pi to one hundred decimal places from this formula.
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.” The great Leonhard Euler, born in 1707, popularized this designation, now known to any schoolchild.
Before the era of computers, mathematicians focused on calculating as many signs as possible. In this regard, sometimes funny things arose. Amateur mathematician W. Shanks calculated 707 digits of Pi in 1875. These seven hundred signs were immortalized on the wall of the Palais des Discoverys in Paris in 1937. However, nine years later, observant mathematicians discovered that only the first 527 characters were correctly calculated. The museum had to incur significant expenses to correct the error - now all the figures 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, was enormous in size, 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 machine 70 hours.
As computers improved, our knowledge of Pi moved 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 exceeded the 10 trillion character mark.
Where else can you meet Pi?
So, often our knowledge about the number Pi remains at the school level, and we know for sure that this number is irreplaceable primarily in geometry.
In addition to formulas for the length and area of a circle, the number Pi is used in formulas for ellipses, spheres, cones, cylinders, ellipsoids, and so on: in some places the formulas are simple and easy to remember, but in others 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 the series, Pi appears most unexpectedly in the famous Riemann zeta function. It’s impossible to talk about it in a nutshell, let’s just say that someday the number Pi will help find a formula for calculating prime numbers.
And absolutely surprisingly: Pi appears in two of the most beautiful “royal” formulas of mathematics - Stirling’s formula (which helps to find the approximate value of the factorial and gamma function) and Euler’s formula (which connects as many as five mathematical constants).
However, the most unexpected discovery awaited mathematicians in probability theory. The number Pi is also there.
For example, the probability that two numbers will be relatively prime is 6/PI^2.
Pi appears in Buffon's needle-throwing problem, formulated in the 18th century: what is the probability that a needle thrown onto a lined piece of paper 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 normal distribution probabilities appears in the equation of the famous Gauss curve. Does this mean that Pi is even more fundamental than simply the ratio of circumference to diameter?
We can also meet Pi in physics. 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 appears in the arrangement of the electron orbitals of the hydrogen atom. And what is again most incredible is that the number Pi 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, on which the film of the same name is based, aliens tell 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 written.
This novel actually reflected a mystery that has occupied the minds of mathematicians all over the world: is Pi a normal number in which the digits are scattered with equal frequency, or is there something wrong with this number? And although scientists are inclined to the first option (but cannot prove it), the number Pi looks very mysterious. A Japanese man once calculated how many times the numbers 0 to 9 occur in the first trillion digits of Pi. And I saw that the numbers 2, 4 and 8 were more common than the others. This may be one of the hints that Pi is not entirely normal, and the numbers in it are indeed not random.
Let's remember everything we read above and ask ourselves, what other irrational and transcendental number is so often found in the real world?
And there are more 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 main character of the American TV series “Suspect,” Professor Finch, told students that due to the infinity of the number Pi, any combination of numbers can be found in it, ranging from the numbers of your date of birth to more complex numbers. For example, at position 762 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 at the 17,387,594,880th digit.
All this means that in the infinity of the number Pi 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 such exists.
By the way, about the Bible. The famous popularizer of mathematics, Martin Gardner, stated in 1966 that the millionth digit of Pi (at that time still unknown) 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 verse (3-14-16) the seventh word contains five letters. The millionth figure was reached eight years later. It was the number five.
Is it worth asserting after this that the number Pi is random?
The history of the number Pi begins in Ancient Egypt and goes in parallel with the development of all mathematics. This is the first time we meet this quantity within the walls of the school.
The number Pi is perhaps the most mysterious of the infinite number of others. Poems are dedicated to him, artists depict him, and even a film was made about him. In our article we will look at the history of development and calculation, as well as the areas of application of the Pi constant in our lives.
Pi is a mathematical constant equal to the ratio of the circumference of a circle to the length of its diameter. It was originally called the Ludolph number, and it was proposed to be denoted by the letter Pi by the British mathematician Jones in 1706. After the work of Leonhard Euler in 1737, this designation became generally accepted.
Pi is an irrational number, meaning its value cannot be accurately expressed as a fraction m/n, where m and n are integers. This was first proven by Johann Lambert in 1761.
The history of the development of the number Pi goes back about 4000 years. Even the ancient Egyptian and Babylonian mathematicians knew that the ratio of the circumference to the diameter is the same for any circle and its value is slightly more than three.
Archimedes proposed a mathematical method for calculating Pi, in which he inscribed regular polygons in a circle and described it around it. According to his calculations, Pi was approximately equal to 22/7 ≈ 3.142857142857143.
In the 2nd century, Zhang Heng proposed two values for Pi: ≈ 3.1724 and ≈ 3.1622.
Indian mathematicians Aryabhata and Bhaskara found an approximate value of 3.1416.
The most accurate approximation of Pi for 900 years was a calculation by Chinese mathematician Zu Chongzhi in the 480s. He deduced that Pi ≈ 355/113 and showed that 3.1415926< Пи < 3,1415927.
Before the 2nd millennium, no more than 10 digits of Pi were calculated. Only with development mathematical analysis, and especially with the discovery of the series, subsequent major advances in the calculation of the constant were made.
In the 1400s, Madhava was able to calculate Pi=3.14159265359. His record was broken by the Persian mathematician Al-Kashi in 1424. In his work “Treatise on the Circle,” he cited 17 digits of Pi, 16 of which turned out to be correct.
The Dutch mathematician Ludolf van Zeijlen reached 20 numbers in his calculations, devoting 10 years of his life to this. After his death, 15 more digits of Pi were discovered in his notes. He bequeathed that these numbers be carved on his tombstone.
With the advent of computers, the number Pi today has several trillion digits and this is not the limit. But, as Fractals for the Classroom points out, as important as Pi is, “it is difficult to find areas in scientific calculations that require more than twenty decimal places.”
In our life, the number Pi is used in many scientific fields. Physics, electronics, probability theory, chemistry, construction, navigation, pharmacology - these are just a few of them that are simply impossible to imagine without this mysterious number.
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Based on materials from the site Calculator888.ru - Pi number - meaning, history, who invented it.
Math enthusiasts around the world eat a piece of pie every year on the fourteenth of March - after all, it 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 since then, but does Pi still have any secrets? From ancient origin until the uncertain future, here are some of the most interesting facts about Pi.
Memorizing Pi
The record for memorizing decimal numbers belongs to Rajvir Meena from India, who managed to remember 70,000 digits - he set the record on March 21, 2015. Previously, the record holder was Chao Lu from China, who managed to remember 67,890 digits - this record was set in 2005. The unofficial record holder is Akira Haraguchi, who recorded himself on video repeating 100,000 digits in 2005 and recently published a video where he manages to remember 117,000 digits. The record would become official only 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. Math enthusiasts love to memorize the number Pi. Many people use various mnemonic techniques, for example poetry, where the number of letters in each word matches the digits of Pi. Each language has its own versions of similar phrases that help you remember both the first few numbers and the whole hundred.
There is a Pi language
Mathematicians, passionate about literature, 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 entirely written in Pi. Enthusiasts of such creativity write their works in full accordance with the number of letters and the meaning of numbers. This has no practical application, but is quite common and known phenomenon in the circles of enthusiastic scientists.
Exponential growth
Pi is an infinite number, so by definition people will never be able to establish the exact digits of this number. However, the number of decimal places has increased greatly since Pi was first used. The Babylonians also used it, but a fraction of three whole and one eighth was enough for them. The Chinese and the creators of the Old Testament were completely limited to three. By 1665, Sir Isaac Newton had calculated the 16 digits of Pi. By 1719, the French mathematician Tom Fante de Lagny had calculated 127 digits. The advent of computers has radically improved human knowledge of Pi. From 1949 to 1967 the number known to man digits skyrocketed from 2037 to 500,000. Not long ago, Peter Trueb, 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 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 some string, or you can use a protractor and a pencil. The downside to using a can is that it needs to be round and accuracy will be determined by how well a person can wrap the rope around it. You can draw a circle with a protractor, but this also requires skill and precision, as an uneven circle can seriously distort your measurements. More exact method involves the use of geometry. Divide the circle into many segments, like a pizza into slices, and then calculate the length of a straight line that would turn each segment into an isosceles triangle. The sum of the sides will give the approximate number 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, however, these simple experiments allow you to understand in more detail what the number Pi is 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. Babylonian tablets calculate Pi as 3.125, and an Egyptian mathematical papyrus shows the number 3.1605. In the Bible, Pi is given in the obsolete length of cubits, and the Greek mathematician Archimedes used the Pythagorean theorem, a geometric relationship between the length of the sides of a triangle and the area of the figures inside and outside the circles, to describe Pi. Thus, we can say with confidence that Pi is one of the most ancient mathematical concepts, although the exact name given number and appeared relatively recently.
New look at Pi
Even before the number Pi began to be correlated with circles, mathematicians already had many ways to even name this number. For example, in ancient mathematics textbooks one can find a phrase in Latin that 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 - this only happened in a book by a lesser-known mathematician, William Jones. He used it already in 1706, but it went unnoticed for a long time. Over time, scientists adopted this name, and now it is the most famous version of the name, although it was previously also called the Ludolf number.
Is Pi a normal number?
Pi is definitely a strange number, but how much does it follow normal mathematical laws? Scientists have already resolved many questions related to this irrational number, but some mysteries remain. For example, it is not known how often all the numbers are used - the numbers 0 to 9 should be used in equal proportion. However, statistics can be traced from the first trillions of 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 quite possible that further development science will help shed light on them, but this moment it remains beyond human intellect.
Pi sounds divine
Scientists cannot answer some questions about the number Pi, however, every year they understand its essence better and better. Already in the eighteenth century, the irrationality of this number was proven. In addition, the number has been proven to be transcendental. This means no a certain formula, which would allow us to calculate Pi using rational numbers. 
Dissatisfaction with the number Pi
Many mathematicians are simply in love with Pi, but there are also those who believe that these numbers are not particularly significant. In addition, they claim that Tau, which is twice the size of Pi, is more convenient to use as an irrational number. Tau shows the relationship between circumference and radius, which some believe represents a more logical method of calculation. However, it is impossible to unambiguously determine anything in this matter, and one and the other will always have supporters, both methods have the right to life, so it’s just interesting fact, and not a reason to think that you shouldn’t use Pi.
