***
What is common between a wheel from Lada Priora, a wedding ring and a saucer of your cat? Of course, you will say beauty and style, but I dare to argue with you. Pi! This is a number that unites all circles, circles and roundness, which include, in particular, my mother's ring, and the wheel from my father's favorite car, and even the saucer of my beloved cat Murzik. I'm willing to bet that in the ranking of the most popular physical and mathematical constants, the number Pi will undoubtedly take the first line. But what is behind it? Maybe some terrible curses of 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 circumference). For those who have gone through mathematics for a long time, and besides, past, we recall that the number Pi is the ratio of the circumference of a circle to its diameter. The value is a constant, that is, it is constant for any circle, regardless of its radius. People have known about this since ancient times. So in ancient Egypt, the number Pi was taken equal to the ratio 256/81, and in the Vedic texts the value 339/108 is given, while Archimedes suggested the ratio 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, respectively, and irrational. This means that it cannot be represented as a simple fraction. If it is expressed in terms of decimal, then the sequence of digits after the decimal point will rush to infinity, moreover, without periodically repeating. What does all of this mean? Very simple. Do you want to know the phone number of the girl you like? It can certainly be found in the sequence of digits after the decimal point of Pi.
Phone can be viewed here ↓
Pi number up to 10000 characters.
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 look.
In general, it can be not only a phone number, but any information encoded using numbers. For example, if we represent 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, curses of mathematicians in π are also present, and not only mathematicians. In a word, Pi has everything, even thoughts that will visit your bright head tomorrow, the day after tomorrow, in a year, or maybe in two. This is very hard to believe, but even if we pretend to believe it, it will be even more difficult to get information from there and decipher it. So instead of delving into these numbers, it might be easier to approach the girl you like and ask her for a number? .. But for those who are not looking for easy ways, well, or just interested in what the number Pi is, I offer several ways to calculations. Count on health.
What is the value of Pi? Methods for its calculation:
1. Experimental method. If pi is the ratio of a circle's circumference to its diameter, then perhaps the first and most obvious way to find our mysterious constant would be to manually take all 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 division into a column. A saucepan or a jar of cucumbers can act as a measured sample, it doesn’t matter, the main thing? so that the base is a circle.
The considered calculation method is the simplest, but, unfortunately, it has two significant drawbacks that affect the accuracy of the resulting Pi number. Firstly, the error of measuring instruments (in our case, this is a ruler with a thread), and secondly, there is no guarantee that the circle we measure will have the correct shape. Therefore, it is not surprising that mathematics has given us many other methods for calculating π, where there is no need to make accurate measurements.
2. Leibniz series. There are several infinite series that allow you to accurately calculate the number of pi to a large number of 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 the one on top) and one number from the sequence of odd numbers in the denominator (this is the one on the bottom), 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?
3. The Nilakanta series. No time fiddling around with Leibniz next? There is an alternative. The Nilakanta series, although it is a bit more complicated, allows us to get the desired result faster. 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 carefully look at the given initial fragment of the series, everything becomes clear, and comments are superfluous. On this we go further.
4. Monte Carlo method A rather interesting method for calculating pi is the Monte Carlo method. Such an extravagant name he got in honor of the city of the same name in the kingdom of Monaco. And the reason for this is random. No, it was not named by chance, it's just that the method is based on random numbers, and what could be more random than the numbers that fall out on the Monte Carlo casino roulettes? The calculation of pi is not the only application of this method, as in the fifties it was used in the calculations of the hydrogen bomb. But let's not digress.
Let's take a square with a side equal to 2r, and inscribe in it a circle with a radius r. Now if you randomly put dots in a square, then the probability P that a point fits into a circle is the ratio of the areas of the circle and the square. P \u003d S cr / S q \u003d 2πr 2 / (2r) 2 \u003d π / 4.
Now from here we express the number Pi π=4P. It remains only to obtain experimental data and find the probability P as the ratio of hits in the circle N cr to hit the square N sq.. In general, the calculation formula will look like this: π=4N cr / N sq.
I would like to note that in order to implement this method, it is not necessary to go to the casino, it is enough to use any more or less decent programming language. Well, the accuracy of the results will depend on the number of points set, respectively, the more, the more accurate. I wish you good luck 😉
Tau number (instead of conclusion).
People who are far from mathematics most likely do not know, but it so happened that the number Pi has a brother who is twice as large as it. This is the number Tau(τ), and if Pi is the ratio of the circumference to the diameter, then Tau is the ratio of that length to the radius. And today there are proposals by some mathematicians to abandon the number Pi and replace it with Tau, since this is in many ways more convenient. But so far these are only proposals, and as Lev Davidovich Landau said: "A new theory begins to dominate when the supporters of the old one die out."
), 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 signs after aim: π ≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 306 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606 606AR 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930 381 964 428 810 975 665 933 446 128 475 648 233 786 783 165 271 201 909 145 648 566 923 460 213 393 607 260 249 141 273 724 587 006 606 315 588 174 881 520 920 962 829 254 091 715 364 367 892 590 360 011 330 548 820 466 521 384 146 951 941 511 609 433 057 270 365 759 591 9 381 932 611 793 105 118 548 074 462 379 962 749 567 351 885 752 724 891 227 938 183 011 949 129 833 673 362…
Properties
Ratios
There are many formulas with the number π:
- Wallis formula:
- Euler's identity:
- T. n. "Poisson integral" or "Gauss integral"
Transcendence and irrationality
Unresolved issues
- It is not known whether the numbers π and e algebraically independent.
- It is not known whether the numbers π + e , π − e , π e , π / e , π e , π π , e e transcendent.
- Until now, nothing is known about the normality of the number π; it is not even known which of the digits 0-9 occur in the decimal representation of the number π an infinite number of times.
Calculation history
and Chudnovsky
Mnemonic rules
In order not to 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 engage in 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 ( ignoring punctuation marks) and write down these numbers in a row - not forgetting the decimal point after the first digit "3", of course. Get an approximate number of Pi.
This I know and remember perfectly: And many signs are superfluous to me, in vain.
Who, jokingly, and soon wishes Pi to know the number - already knows!
So Misha and Anyuta ran to Pi to find out the number they wanted.
(The second mnemonic is correct (with rounding of the last digit) only when using pre-reform orthography: when counting the number of letters in words, hard signs must be taken into account!)
Another version of this mnemonic notation:
This I know and remember very well:
Pi many signs are superfluous to me, in vain.
Let's trust the vast knowledge
Those who have counted, numbers armada.
If you follow the poetic size, 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
funny facts
Notes
See what "Pi" is in other dictionaries:
number- Reception Source: GOST 111 90: Sheet glass. Specifications original document See also related terms: 109. Number of betatron oscillations ... Dictionary-reference book of terms of normative and technical documentation
Ex., s., use. very often Morphology: (no) what? numbers for what? number, (see) what? number than? number about what? about the number; pl. what? numbers, (no) what? numbers for what? numbers, (see) what? numbers than? numbers about what? about mathematics numbers 1. Number ... ... Dictionary of Dmitriev
NUMBER, numbers, pl. numbers, numbers, numbers, cf. 1. A concept that serves as an expression of quantity, something with the help of which objects and phenomena are counted (mat.). Integer. Fractional number. named number. Prime number. (see simple1 in 1 value).… … Explanatory Dictionary of Ushakov
An abstract designation, devoid of special content, of any member of a certain series, in which this member is preceded or followed by some other definite member; an abstract individual feature that distinguishes one set from ... ... Philosophical Encyclopedia
Number- Number is a grammatical category that expresses the quantitative characteristics of objects of thought. The grammatical number is one of the manifestations of a more general linguistic category of quantity (see the Linguistic category) along with a lexical manifestation (“lexical ... ... Linguistic Encyclopedic Dictionary
A number approximately equal to 2.718, which is often found in mathematics and science. For example, during the decay of a radioactive substance after time t, a fraction equal to e kt remains from the initial amount of substance, where k is a number, ... ... Collier Encyclopedia
BUT; pl. numbers, villages, slam; cf. 1. A unit of account expressing one or another quantity. Fractional, integer, simple hours. Even, odd hours. Count as round numbers (approximately, counting as whole units or tens). Natural hours (positive integer ... encyclopedic Dictionary
Wed quantity, count, to the question: how much? and the very sign expressing quantity, the figure. Without number; no number, no count, many many. Put the appliances according to the number of guests. Roman, Arabic or church numbers. Integer, contra. fraction. ... ... Dahl's Explanatory Dictionary
NUMBER, a, pl. numbers, villages, slam, cf. 1. The basic concept of mathematics is the value, with the help of which the swarm is calculated. Integer hours Fractional hours Real hours Complex hours Natural hours (positive integer). Simple hours (natural number, not ... ... Explanatory dictionary of Ozhegov
NUMBER "E" (EXP), an irrational number that serves as the basis of natural LOGARITHMS. This real decimal number, an infinite fraction equal to 2.7182818284590...., is the limit of the expression (1/) as n goes to infinity. In fact,… … Scientific and technical encyclopedic dictionary
14 Mar 2012
On March 14, mathematicians celebrate one of the most unusual holidays - International Pi Day. This date was not chosen by chance: the numerical expression π (Pi) is 3.14 (3rd month (March) 14th day).
For the first time, schoolchildren come across this unusual number already in the elementary grades when studying a circle and a circle. The number π is a mathematical constant that expresses the ratio of the circumference of a circle to the length of its diameter. That is, if we take a circle with a diameter equal to one, then the circumference will be equal to the number "Pi". The number π has an infinite mathematical duration, but in everyday calculations they use a simplified spelling of the number, leaving only two decimal places, - 3.14.
In 1987 this day was celebrated for the first time. Physicist Larry Shaw from San Francisco noticed that in the American system of writing dates (month / day), the date March 14 - 3/14 coincides with the number π (π \u003d 3.1415926 ...). Celebrations usually start at 1:59:26 p.m. (π = 3.14 15926 …).
History of Pi
It is assumed that the history of the number π begins in ancient Egypt. Egyptian mathematicians determined the area of a circle with a diameter D as (D-D/9) 2 . From this entry it can be seen that at that time the number π was equated to the fraction (16/9) 2, or 256/81, i.e. π 3.160...
In the VI century. BC. In India, there are records in the religious book of Jainism, indicating that the number π at that time was taken equal to the square root of 10, which gives a fraction of 3.162 ...
In the III century. BC Archimedes in his short work "Measurement of the circle" substantiated three positions:
- Any circle is equal in size to a right triangle, the legs of which are respectively equal to the circumference and its radius;
- The areas of a circle are related to a square built on a diameter as 11 to 14;
- The ratio of any circle to its diameter is less than 3 1/7 and greater than 3 10/71.
Archimedes substantiated the latter position by sequentially calculating the perimeters of regular inscribed and circumscribed polygons with doubling the number of their sides. According to the exact calculations of Archimedes, the ratio of circumference to diameter is between 3*10/71 and 3*1/7, which means that the number "pi" is 3.1419... The true value of this ratio is 3.1415922653...
In the 5th century BC. Chinese mathematician Zu Chongzhi found a more accurate value for this number: 3.1415927...
In the first half of the XV century. astronomer and mathematician-Kashi calculated π with 16 decimal places.
A century and a half later, in Europe, F. Viet found the number π with only 9 correct decimal places: he made 16 doublings of the number of sides of polygons. F. Wiet was the first to notice that π can be found using the limits of some series. This discovery was of great importance, it made it possible to calculate π with any accuracy.
In 1706, the English mathematician W. Johnson introduced the notation for the ratio of the circumference of a circle to its diameter and designated it with the modern symbol π, the first letter of the Greek word periferia-circle.
For a long period of time, scientists around the world have been trying to unravel the mystery of this mysterious number.
What is the difficulty in calculating the value of π?
The number π is irrational: it cannot be expressed as a fraction p/q, where p and q are integers, this number cannot be the root of an algebraic equation. It is impossible to specify an algebraic or differential equation whose root is π, therefore this number is called transcendental and is calculated by considering a process and refined by increasing the steps of the process under consideration. Multiple attempts to calculate the maximum number of digits of the number π have led to the fact that today, thanks to modern computing technology, it is possible to calculate a sequence with an accuracy of 10 trillion digits after the decimal point.
The digits of the decimal representation of the number π are quite random. In the decimal expansion of a number, you can find any sequence of digits. It is assumed that in this number in encrypted form there are all written and unwritten books, any information that can only be represented is in the number π.
You can try to solve the mystery of this number yourself. Writing down the number "Pi" in full, of course, will not work. But I propose to the most curious to consider the first 1000 digits of the number 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
Remember the number "Pi"
Currently, with the help of computer technology, ten trillion digits of the number "Pi" has been calculated. The maximum number of digits that a person could remember is one hundred thousand.
To memorize the maximum number of characters of the number "Pi", various poetic "memory" are used, in which words with a certain number of letters are arranged in the same sequence as the numbers in the number "Pi": 3.1415926535897932384626433832795 .... To restore the number, you need to count the number of characters in each of the words and write it down in order.
So I know the number called "Pi". Well done! (7 digits)
So Misha and Anyuta came running
Pi to know the number they wanted. (11 digits)
This I know and remember very well:
Pi many signs are superfluous to me, in vain.
Let's trust the vast knowledge
Those who have counted, numbers armada. (21 digits)
Once at Kolya and Arina
We ripped the feather beds.
White fluff flew, circled,
Courageous, froze,
blissed out
He gave us
Headache of old women.
Wow, dangerous fluff spirit! (25 characters)
You can use rhyming lines that help you remember the right number.
So that we don't make mistakes
It needs to be read correctly:
ninety two and six
If you try hard
You can immediately read:
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 keep repeating:
"Three, fourteen, fifteen,
Nine, twenty-six and five."
Do you have any questions? Want to know more about Pi?
To get help from a tutor, register.
The first lesson is free!
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 videotaped his repetition of 100,000 digits in 2005 and recently posted 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.
There is a Pi language
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 figure out 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. The Chinese and the creators of the Old Testament were completely limited to the 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 of digits known to man 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 an 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 of this number has 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 old 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 resolved 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 at the moment this remains beyond the limits of human intelligence.
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.
Number value(pronounced "pi") is a mathematical constant equal to the ratio
Denoted by the letter of the Greek alphabet "pi". old name - Ludolf number.
What is pi equal to? In simple cases, it is enough to know the first 3 characters (3.14). But for more
complex cases and where greater accuracy is needed, it is necessary to know more than 3 digits.
What is pi? The first 1000 decimal places of pi are:
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...
Under normal conditions, the approximate value of pi can be calculated by following the points,
below:
- Take a circle, wrap the thread around its edge once.
- We measure the length of the thread.
- We measure the diameter of the circle.
- Divide the length of the thread by the length of the diameter. We got the number pi.
Pi properties.
- pi- irrational number, i.e. the value of pi cannot be expressed exactly in the form
fractions m/n, where m and n are integers. This shows that the decimal representation
pi never ends and it is not periodic.
- pi is a transcendental number, i.e. it cannot be a root of any polynomial with integers
coefficients. In 1882, Professor Königsberg proved the transcendence pi, a
later, professor at the University of Munich Lindemann. Proof simplified
Felix Klein in 1894.
- since in Euclidean geometry the area of a circle and the circumference of a circle are functions of pi,
then the proof of the transcendence of pi put an end to the dispute about the squaring of the circle, which lasted more than
2.5 thousand years.
- pi is an element of the period ring (that is, a computable and arithmetic number).
But no one knows whether it belongs to the ring of periods.
Pi formula.
- François Viet:
- Wallis formula:
- Leibniz series:
- Other rows:
