Pi is calculated. Calculating the value of pi

If you compare circles of different sizes, you will notice the following: the sizes of different circles are proportional. This means that when the diameter of a circle increases by a certain number of times, the length of this circle also increases by the same number of times. Mathematically this can be written like this:

where C1 and C2 are the lengths of two different circles, and d1 and d2 are their diameters.
This relationship works in the presence of a coefficient of proportionality - the constant π already familiar to us. From relation (1) we can conclude: the length of a circle C is equal to the product of the diameter of this circle and a proportionality coefficient π independent of the circle:

C = π d.

This formula can also be written in another form, expressing the diameter d through the radius R of a given circle:

С = 2π R.

It is precisely this formula that is a guide to the world of circles for seventh graders.

Since ancient times, people have tried to establish the value of this constant. For example, the inhabitants of Mesopotamia calculated the area of ​​a circle using the formula:

Where does π = 3 come from?

IN ancient Egypt the value for π was more accurate. In 2000-1700 BC, a scribe called Ahmes compiled a papyrus in which we find recipes for resolving various practical problems. So, for example, to find the area of ​​a circle, he uses the formula:

From what reasons did he arrive at this formula? – Unknown. Probably based on his observations, however, as other ancient philosophers did.

In the footsteps of Archimedes

Which of the two numbers is greater than 22/7 or 3.14?
- They are equal.
- Why?
- Each of them is equal to π.
A. A. Vlasov. From the Examination Card.

Some people believe that the fraction 22/7 and the number π are identically equal. But this is a misconception. In addition to the above incorrect answer in the exam (see epigraph), you can also add one very entertaining puzzle to this group. The task reads: “arrange one match so that the equality becomes true.”

The solution would be this: you need to form a “roof” for the two vertical matches on the left, using one of the vertical matches in the denominator on the right. You will get a visual image of the letter π.

Many people know that the approximation π = 22/7 was determined by the ancient Greek mathematician Archimedes. In honor of this, such an approximation is often called the “Archimedean” number. Archimedes managed not only to establish an approximate value for π, but also to find the accuracy of this approximation, namely, to find a narrow numerical interval, to which the value π belongs. In one of his works, Archimedes proves a chain of inequalities, which in a modern way would look like this:

can be written more simply: 3,140 909< π < 3,1 428 265...

As we see from the inequalities, Archimedes found quite exact value with an accuracy of 0.002. The most surprising thing is that he found the first two decimal places: 3.14... This is the value we most often use in simple calculations.

Practical Application

Two people are traveling on a train:
- Look, the rails are straight, the wheels are round.
Where is the knock coming from?
- Where from? The wheels are round, but the area
circle pi er square, that’s the square that knocks!

As a rule, they become acquainted with this amazing number in the 6th-7th grade, but study it more thoroughly by the end of the 8th grade. In this part of the article we will present the main and most important formulas, which will be useful to you in solving geometric problems, just to begin with, let’s agree to take π as 3.14 for ease of calculation.

Perhaps the most famous formula among schoolchildren, in which π is used, this is the formula for the length and area of ​​a circle. The first, the formula for the area of ​​a circle, is written as follows:

where S is the area of ​​the circle, R is its radius, D is the diameter of the circle.

The circumference of a circle, or, as it is sometimes called, the perimeter of a circle, is calculated by the formula:

C = 2 π R = π d,

where C is the circumference, R is the radius, d is the diameter of the circle.

It is clear that the diameter d is equal to two radii R.

From the formula for circumference, you can easily find the radius of the circle:

where D is the diameter, C is the circumference, R is the radius of the circle.

This basic formulas, which every student should know. Also, sometimes it is necessary to calculate the area not of the entire circle, but only of its part - the sector. Therefore, we present it to you - a formula for calculating the area of ​​a sector of a circle. It looks like this:

where S is the area of ​​the sector, R is the radius of the circle, α is central angle in degrees.

So mysterious 3.14

Indeed, it is mysterious. Because in honor of these magical numbers they organize holidays, make films, hold public events, write poetry and much more.

For example, in 1998, a film by American director Darren Aronofsky called “Pi” was released. The film received many awards.

Every year on March 14 at 1:59:26 a.m., people interested in mathematics celebrate "Pi Day." For the holiday, people prepare a round cake, sit down to round table and discuss Pi and solve problems and puzzles related to Pi.

Poets also paid attention to this amazing number; an unknown person wrote:
You just have to try and remember everything as it is - three, fourteen, fifteen, ninety-two and six.

Let's have some fun!

We offer you interesting puzzles with the number Pi. Unravel the words that are encrypted below.

1. π r

2. π L

3. π k

Answers: 1. Feast; 2. File; 3. Squeak.

(), and it became generally accepted after the work of Euler. This designation comes from initial letter 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 12 8 475 648 233 786 783 165 271 201 909 145 648 566 923 460 348 610 454 326 648 213 393 607 260 249 141 273 724 587 006 606 315 588 174 881 520 920 962 829 254 091 715 364 367 892 590 360 011 330 530 8 820 466 521 384 146 951 941 511 609 433 057 270 365 759 591 953 092 186 117 381 932 611 793 105 118 548 074 462 379 962 749 567 351 885 752 724 891 227 938 183 011 949 129 833 673 362…

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 are found in the decimal representation of the number π infinite number once.

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. So that 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 decimal point after the first number “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 comply poetic meter, you can remember pretty quickly:

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. 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. Concept, expressive quantity, that by which objects and phenomena are counted (mat.). Integer. Fractional number. Named number. Prime number. (see simple 1 in 1 value).… … Ushakov's Explanatory Dictionary

An abstract, devoid of special content designation of any member of a certain series, in which this member is preceded or followed by some other. specific member; abstract individual trait, distinguishing one set from... ... Philosophical Encyclopedia

Number- Number grammatical category, expressing the quantitative characteristics of objects of thought. Grammatical number 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, during the collapse radioactive substance after time t, a portion of the initial amount of substance remains equal to e kt, 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 relationship is usually denoted Greek letter(“pi” is the initial letter 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 after another hundred seconds extra years 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.

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 threads, 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.

Draw a square on a piece 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

Figure 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

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 1

REM "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:

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

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 Oh. 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 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 2

REM "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:

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 3

REM "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 for various values ​​of the parameter n. The resulting number values ​​are written in the table:

***

What does a wheel from a Lada Priora have in common? wedding ring and your cat's saucer? Of course, you will say beauty and style, but I dare to argue with you. Pi number! This is a number that unites all circles, circles and roundness, which in particular include my mother’s ring, the wheel from my father’s favorite car, and even the saucer of my favorite cat Murzik. I'm willing to bet that in the ranking of the most popular physical and mathematical constants, Pi will undoubtedly take first place. But what is hidden behind it? Maybe some terrible curse words from mathematicians? Let's try to understand this issue.

What is the number "Pi" and where did it come from?

Modern number designation π (Pi) appeared thanks to the English mathematician Johnson in 1706. This is the first letter of the Greek word περιφέρεια (periphery, or circle). For those who took mathematics a long time ago, and besides, by no means, let us remind you that the number Pi is the ratio of the circumference of a circle to its diameter. The value is a constant, that is, constant for any circle, regardless of its radius. People knew about this in ancient times. So in ancient Egypt the number Pi was taken equal to the ratio 256/81, and in Vedic texts the value is given as 339/108, while Archimedes proposed a ratio of 22/7. But neither these nor many other ways of expressing the number Pi gave an accurate result.

It turned out that the number Pi is transcendental and, accordingly, irrational. This means that it cannot be represented as a simple fraction. If we express it in decimal terms, then the sequence of digits after the decimal point will rush to infinity, and, moreover, without periodically repeating itself. What does this all mean? Very simple. Do you want to know the phone number of the girl you like? It can probably be found in the sequence of digits after the decimal point of Pi.

You can see the phone number here ↓

Pi number accurate to 10,000 digits.

π= 3,
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989..

Didn't find it? Then take a look.

In general, this can be not only a phone number, but any information encoded using numbers. For example, if you imagine all the works of Alexander Sergeevich Pushkin in digital form, then they were stored in the number Pi even before he wrote them, even before he was born. In principle, they are still stored there. By the way, the curses of mathematicians in π are also present, and not only mathematicians. In a word, the number Pi contains everything, even thoughts that will visit your bright head tomorrow, the day after tomorrow, in a year, or maybe in two. This is very difficult to believe, but even if we imagine that we believe it, it will be even more difficult to obtain information from it and decipher it. So, instead of delving into these numbers, maybe it’s easier to approach the girl you like and ask her number?.. But for those who are not looking for easy ways, or are simply interested in what the number Pi is, I offer several ways calculations. Consider it healthy.

What is Pi equal to? Methods for calculating it:

1. Experimental method. If Pi is the ratio of the circumference of a circle to its diameter, then the first, perhaps most obvious, way to find our mysterious constant will be to manually make all the measurements and calculate Pi using the formula π=l/d. Where l is the circumference of the circle, and d is its diameter. Everything is very simple, you just need to arm yourself with a thread to determine the circumference, a ruler to find the diameter, and, in fact, the length of the thread itself, and a calculator if you have problems with long division. The role of the sample to be measured can be a saucepan or a jar of cucumbers, it doesn’t matter, the main thing is? so that there is a circle at the base.

The considered method of calculation is the simplest, but, unfortunately, it has two significant drawbacks that affect the accuracy of the resulting Pi number. Firstly, the error of the measuring instruments (in our case, this is a ruler with a thread), and secondly, there is no guarantee that the circle we are measuring will have correct form. Therefore, it is not surprising that mathematics has given us many other methods for calculating π, where there is no need to make precise measurements.

2. Leibniz series. There are several infinite series that allow you to accurately calculate Pi up to large quantity decimal places. One of the simplest series is the Leibniz series. π = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...
It’s simple: we take fractions with 4 in the numerator (this is what’s on top) and one number from the sequence of odd numbers in the denominator (this is what’s below), sequentially add and subtract them with each other and get the number Pi. The more iterations or repetitions of our simple actions, the more accurate the result. Simple, but not effective; by the way, it takes 500,000 iterations to get the exact value of Pi to ten decimal places. That is, we will have to divide the unfortunate four as many as 500,000 times, and in addition to this, we will have to subtract and add the results obtained 500,000 times. Want to try it?

3. Nilakanta series. Don't have time to tinker with the Leibniz series? There is an alternative. The Nilakanta series, although it is a little more complicated, allows us to quickly get the desired result. π = 3 + 4/(2*3*4) — 4/(4*5*6) + 4/(6*7*8) — 4/(8*9*10) + 4/(10*11 *12) - (4/(12*13*14) ... I think if you look closely at the above initial fragment series, everything becomes clear, and comments are unnecessary. Let's move on with this.

4. Monte Carlo method A rather interesting method for calculating Pi is the Monte Carlo method. It got such an extravagant name in honor of the city of the same name in the kingdom of Monaco. And the reason for this is coincidence. No, it was not named by chance, the method is simply based on random numbers, and what could it be more random than numbers that appear on the roulette tables of the Monte Carlo casino? Calculating Pi is not the only application of this method; in the fifties it was used in calculations hydrogen bomb. But let's not get distracted.

Take a square with a side equal to 2r, and inscribe a circle with radius r. Now if you put dots in a square at random, then the probability P The fact that a point falls into a circle is the ratio of the areas of the circle and the square. P=S kr /S kv =2πr 2 /(2r) 2 =π/4.

Now let's express the number Pi from here π=4P. All that remains is to obtain experimental data and find the probability P as the ratio of hits in the circle N cr to hitting the square N sq.. IN general view calculation formula will look like this: π=4N cr / N square.

I would like to note that in order to implement this method, it is not necessary to go to a casino; it is enough to use any more or less decent programming language. Well, the accuracy of the results obtained will depend on the number of points placed; accordingly, the more, the more accurate. I wish you good luck 😉

Tau number (Instead of a conclusion).

People far from mathematics most likely do not know, but it so happens that the number Pi has a brother who is twice its size. This is the number Tau(τ), and if Pi is the ratio of the circumference to the diameter, then Tau is the ratio of this length to the radius. And today there are proposals from some mathematicians to abandon the number Pi and replace it with Tau, since this is in many ways more convenient. But for now these are only proposals, and as Lev Davidovich Landau said: “ New theory begins to dominate when the supporters of the old die out.”

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. Every language has its own variants similar phrases, which help you remember both the first few digits 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 infinite number, so people, by definition, will never be able to establish the exact figures 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. Chinese and creators Old Testament and were completely limited to three. By 1665, Sir Isaac Newton had calculated the 16 digits of Pi. By 1719 French mathematician Tom Fante de Lagny calculated 127 digits. The advent of computers has radically improved human knowledge of Pi. From 1949 to 1967 the number known to man numbers 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 install even more exact figure- since Pi is infinite, there is simply no limit to accuracy, and it can only be limited technical features computer technology.

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. A more accurate method involves using geometry. Divide a circle into many segments, like a pizza into 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 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, nevertheless these simple experiments allow you to understand in more detail what the number Pi actually 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, the number Pi is given in an outdated length - in cubits, and the Greek mathematician Archimedes used the Pythagorean theorem to describe Pi, geometric relationship the lengths of the sides of the triangle and the area of ​​the figures inside and outside the circles. Thus, we can say with confidence that Pi is one of the most ancient mathematical concepts, at least 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 the book less famous 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 known version names, although previously it was also called the Ludolf number.

Is Pi a normal number?

The number Pi is definitely strange, but how much does it obey the normal ones? 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 at the 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, to unambiguously determine something in this issue impossible, and one and the other number will always have supporters, both methods have the right to life, so it’s simple interesting fact, and not a reason to think that you shouldn’t use Pi.