How many decimal places are there in pi? The mysterious number "pi"
One of the most mysterious numbers known to mankind, of course, is the number Π (read - pi). In algebra, this number reflects the ratio of the circumference of a circle to its diameter. Previously, this quantity was called the Ludolph number. How and where the number Pi came from is not known for certain, but mathematicians divide the entire history of the number Π into 3 stages: ancient, classical and the era of digital computers.
The number P is irrational, that is, it cannot be represented as a simple fraction, where the numerator and denominator are integers. Therefore, such a number has no ending and is periodic. The irrationality of P was first proven by I. Lambert in 1761.
In addition to this property, the number P cannot also be the root of any polynomial, and therefore the property is a number; when it was proven in 1882, it put an end to the almost sacred dispute among mathematicians “about the squaring of the circle,” which lasted for 2,500 years.
It is known that the Briton Jones was the first to introduce the designation of this number in 1706. After Euler's works appeared, the use of this notation became generally accepted.
To understand in detail what the number Pi is, it should be said that its use is so widespread that it is difficult to even name an area of science that would do without it. One of the simplest and most familiar school curriculum values is a designation of the geometric period. The ratio of the length of a circle to the length of its diameter is constant and equal to 3.14. This value was known to the most ancient mathematicians in India, Greece, Babylon, and Egypt. The earliest version of the calculation of the ratio dates back to 1900 BC. e. Closer to modern meaning P was calculated by the Chinese scientist Liu Hui, in addition, he invented and quick way such a calculation. Its value remained generally accepted for almost 900 years.
The classical period in the development of mathematics was marked by the fact that in order to establish exactly what the number Pi is, scientists began to use methods of mathematical analysis. In the 1400s, Indian mathematician Madhava used series theory to calculate and determined the period of P to within 11 decimal places. The first European, after Archimedes, who studied the number P and made a significant contribution to its substantiation, was the Dutchman Ludolf van Zeilen, who already determined 15 digits after the decimal point, and in his will he wrote very entertaining words: “... whoever is interested, let him move on.” It was in honor of this scientist that the number P received its first and only name in history.
The era of computer computing has brought new details to the understanding of the essence of the number P. So, in order to find out what the number Pi is, in 1949 the ENIAC computer was first used, one of the developers of which was the future “father” of the theory modern computers J. The first measurement was carried out for 70 hours and gave 2037 digits after the decimal point in the period of the number P. The million digit mark was reached in 1973. In addition, during this period, other formulas were established that reflected the number P. Thus, the Chudnovsky brothers were able to find one that made it possible to calculate 1,011,196,691 digits of the period.
In general, it should be noted that in order to answer the question: “What is Pi?”, many studies began to resemble competitions. Today, supercomputers are already working on the question of what the real number Pi is. interesting facts related to these studies permeate almost the entire history of mathematics.
Today, for example, world championships in memorizing the number P are being held and world records are being recorded, the last one belongs to the Chinese Liu Chao, who named 67,890 characters in just over a day. There is even a holiday of the number P in the world, which is celebrated as “Pi Day”.
As of 2011, 10 trillion digits of the number period have already been established.
There are a lot of mysteries among the PIs. Or rather, these are not even riddles, but a kind of Truth that no one has yet solved in the entire history of mankind...
What is Pi? The PI number is a mathematical “constant” that expresses the ratio of the circumference of a circle to its diameter. At first, out of ignorance, it (this ratio) was considered equal to three, which was a rough approximation, but it was enough for them. But when prehistoric times gave way to ancient times (i.e., already historical), the surprise of inquisitive minds knew no bounds: it turned out that the number three very inaccurately expresses this ratio. With the passage of time and the development of science, this number began to be considered equal to twenty-two sevenths.
The English mathematician Augustus de Morgan once called the number PI “... the mysterious number 3.14159... that crawls through the door, through the window and through the roof.” Tireless scientists continued and continued to calculate the decimal places of the number Pi, which is actually a wildly non-trivial task, because you can’t just calculate it in a column: the number is not only irrational, but also transcendental (these are just such numbers that cannot be calculated by simple equations).
In the process of calculating these same signs, many different scientific methods and entire sciences. But the most important thing is that there are no repetitions in the decimal part of pi, as in the usual periodic fraction, and the number of decimal places is infinite. Today it has been verified that there are indeed no repetitions in 500 billion digits of pi. There is reason to believe that there are none at all.
Since there are no repetitions in the sequence of pi signs, this means that the sequence of pi signs obeys the theory of chaos, or more precisely, the number pi is chaos written in numbers. Moreover, if desired, this chaos can be represented graphically, and there is an assumption that this Chaos is intelligent.
In 1965, the American mathematician M. Ulam, sitting at one boring meeting, with nothing to do, began to write the numbers included in pi on checkered paper. Putting 3 in the center and moving counterclockwise in a spiral, he wrote out 1, 4, 1, 5, 9, 2, 6, 5 and other numbers after the decimal point. Along the way, he circled everything prime numbers in circles. Imagine his surprise and horror when the circles began to line up along straight lines!
In the decimal tail of pi you can find any desired sequence of digits. Any sequence of digits in the decimal places of pi will be found sooner or later. Any!
So what? – you ask. Otherwise... Think about it: if your phone is there (and it is), then there is also the phone number of the girl who didn’t want to give you her number. Moreover, there are credit card numbers, and even all the values of the winning numbers for tomorrow's lottery draw. What is there, in general, all lotteries for many millennia to come. The question is how to find them there...
If you encrypt all the letters with numbers, then in the decimal expansion of the number pi you can find all the world literature and science, and a recipe for making bechamel sauce, and that’s it holy books all religions. This is strict scientific fact. After all, the sequence is INFINITE and the combinations in the number PI are not repeated, therefore it contains ALL combinations of numbers, and this has already been proven. And if everything, then ALL. Including those that correspond to the book you have chosen.
And this again means that it contains not only all world literature, which has already been written (in particular, those books that burned, etc.), but also all the books that still WILL be written. Including your articles on websites. It turns out that this number (the only reasonable number in the Universe!) governs our world. You just need to look at more signs, find the right area and decipher it. This is somewhat akin to the paradox of a herd of chimpanzees hammering away at a keyboard. Given a long enough experiment (you can even estimate the time) they will print all of Shakespeare's plays.
This immediately suggests an analogy with periodically appearing reports that in Old Testament, allegedly, encoded messages to descendants that can be read using clever programs. It is not entirely wise to immediately dismiss such an exotic feature of the Bible; cabalists have been searching for such prophecies for centuries, but I would like to cite the message of one researcher who, using a computer, found words in the Old Testament that there are no prophecies in the Old Testament. Most likely, in a very large text, as well as in the infinite digits of the PI number, it is possible not only to encode any information, but also to “find” phrases that were not originally included there.
For practice, 11 characters after the dot are enough within the Earth. Then, knowing that the radius of the Earth is 6400 km or 6.4 * 1012 millimeters, it turns out that if we discard the twelfth digit in the PI number after the point when calculating the length of the meridian, we will be mistaken by several millimeters. And when calculating the length of the Earth’s orbit when rotating around the Sun (as is known, R = 150 * 106 km = 1.5 * 1014 mm), for the same accuracy it is enough to use the number PI with fourteen digits after the dot, and what’s there to waste - the diameter of our Galaxies are about 100,000 light years away (1 light year is approximately equal to 1013 km) or 1018 km or 1030 mm, and back in the 17th century, 34 digits of the PI number were obtained, excessive for such distances, and them on at the moment calculated to 12411 trillionth digit!!!
The absence of periodically repeating numbers, namely, based on their formula Circumference = Pi * D, the circle does not close, since there is no finite number. This fact can also be closely related to the spiral manifestation in our lives...
There is also a hypothesis that all (or some) universal constants (Planck’s constant, Euler’s number, universal gravitational constant, electron charge, etc.) change their values over time, as the curvature of space changes due to the redistribution of matter or for other reasons unknown to us.
At the risk of incurring the wrath of the enlightened community, we can assume that the PI number considered today, reflecting the properties of the Universe, may change over time. In any case, no one can forbid us to re-find the value of the number PI, confirming (or not confirming) the existing values.
10 interesting facts about PI number
1. The history of numbers goes back more than one thousand years, almost as long as the science of mathematics has existed. Certainly, exact value The numbers were not calculated immediately. At first, the ratio of circumference to diameter was considered equal to 3. But over time, when architecture began to develop, a more accurate measurement was required. By the way, the number existed, but it received a letter designation only in early XVIII century (1706) and comes from initial letters two Greek words meaning "circle" and "perimeter". The letter “π” was given to the number by the mathematician Jones, and it became firmly established in mathematics already in 1737.
2. In different eras and different nations Pi had different meaning. For example, in Ancient Egypt it was equal to 3.1604, among the Indians it acquired a value of 3.162, the Chinese used a number equal to 3.1459. Over time, π was calculated more and more accurately, and when computing technology, that is, a computer, appeared, it began to number more than 4 billion characters.
3. There is a legend, or rather experts believe, that the number Pi was used in the construction of the Tower of Babel. However, it was not the wrath of God that caused its collapse, but incorrect calculations during construction. Like, the ancient masters were wrong. A similar version exists regarding the Temple of Solomon.
4. It is noteworthy that they tried to introduce the value of Pi even at the state level, that is, through law. In 1897, the state of Indiana prepared a bill. According to the document, Pi was 3.2. However, scientists intervened in time and thus prevented the mistake. In particular, Professor Perdue, who was present at the legislative meeting, spoke out against the bill.
5. Interestingly, several numbers in the infinite sequence Pi have their own name. So, six nines of Pi are named after the American physicist. Richard Feynman once gave a lecture and stunned the audience with a remark. He said he wanted to memorize the digits of Pi up to six nines, only to say "nine" six times at the end of the story, implying that its meaning was rational. When in fact it is irrational.
6. Mathematicians around the world do not stop conducting research related to the number Pi. It is literally shrouded in some mystery. Some theorists even believe that it contains universal truth. To share knowledge and new information Oh Pi, we organized a Pi Club. It’s not easy to join; you need to have an extraordinary memory. Thus, those wishing to become a member of the club are examined: a person must recite from memory as many signs of the number Pi as possible.
7. They even came up with various techniques to remember the number Pi after the decimal point. For example, they come up with entire texts. In them, words have the same number of letters as the corresponding number after the decimal point. To make it even easier to remember such a long number, they compose poems according to the same principle. Members of the Pi Club often have fun in this way, and at the same time train their memory and intelligence. For example, Mike Keith had such a hobby, who eighteen years ago came up with a story in which each word was equal to almost four thousand (3834) of the first digits of Pi.
8. There are even people who have set records for memorizing Pi signs. So, in Japan, Akira Haraguchi memorized more than eighty-three thousand characters. But the domestic record is not so outstanding. A resident of Chelyabinsk managed to recite by heart only two and a half thousand numbers after the decimal point of Pi.
9. Pi Day has been celebrated for more than a quarter of a century, since 1988. One day, a physicist from the popular science museum in San Francisco, Larry Shaw, noticed that March 14, when written, coincides with the number Pi. In the date, the month and day form 3.14.
10. There is an interesting coincidence. On March 14, the great scientist Albert Einstein, who, as we know, created the theory of relativity, was born.
Absolutely everyone knows what “pi” is. But the number, familiar to everyone from school, arises in many situations that have nothing to do with circles. It can be found in probability theory, in the Stirling formula for calculating the factorial, in solving problems with complex numbers and other unexpected and far from geometry areas of mathematics. The English mathematician Augustus de Morgan once called pi “... the mysterious number 3.14159... that crawls through the door, through the window and through the roof.”
This mysterious number, associated with one of the three classical problems of Antiquity - the construction of a square whose area is equal to the area of a given circle - entails a trail of dramatic historical and curious interesting facts.
- Some interesting facts about Pi
- 1. Did you know that the first person to use the symbol “pi” for the number 3.14 was William Jones from Wales, and this happened in 1706?
- 2. Did you know that the world record for memorizing the number Pi was set on June 17, 2009 by Ukrainian neurosurgeon, Doctor of Medical Sciences, Professor Andrey Slyusarchuk, who retained 30 million of its characters (20 volumes of text) in memory.
- 3. Did you know that in 1996 Mike Keith wrote short story, which is called “Rhythmic Cadenza” (“Cadeic Cadenze”), in its text the length of the words corresponded to the first 3834 digits of Pi.
It is believed that the holiday was invented in 1987 by San Francisco physicist Larry Shaw, who noticed that on March 14 (in American writing - 3.14) at exactly 01:59, the date and time would coincide with the first digits of the number Pi = 3.14159.
The creator of the theory of relativity, Albert Einstein, was also born on March 14, 1879, which makes this day even more attractive for all mathematics lovers.
In addition, mathematicians also celebrate the day of the approximate value of Pi, which falls on July 22 (22/7 in the European date format).
“During this time, they read eulogies in honor of the number Pi and its role in the life of mankind, draw dystopian pictures of a world without Pi, eat pies with the image of the Greek letter Pi or with the first digits of the number itself, solve mathematical puzzles and riddles, and also dance in circles.” , writes Wikipedia.
In numerical terms, Pi begins as 3.141592 and has an infinite mathematical duration.
French scientist Fabrice Bellard calculated the number Pi with record accuracy. This is reported on his official website. The latest record is about 2.7 trillion (2 trillion 699 billion 999 million 990 thousand) decimal places. The previous achievement belongs to the Japanese, who calculated the constant with an accuracy of 2.6 trillion decimal places.
Bellar's calculations took him about 103 days. All calculations were carried out on home computer, the cost of which is around 2000 euros. For comparison, the previous record was set on the T2K Tsukuba System supercomputer, which took about 73 hours to run.
Initially, the number Pi appeared as the ratio of the length of a circle to its diameter, so its approximate value was calculated as the ratio of the perimeter of a polygon inscribed in a circle to the diameter of this circle. Later, more advanced methods appeared. Currently, Pi is calculated using rapidly convergent series, like those proposed by Srinivas Ramanujan in the early 20th century.
Pi was first calculated in binary and then converted to decimal. This was done in 13 days. In total, storing all the numbers requires 1.1 terabytes of disk space.
Such calculations have not only practical significance. So, now there are many unsolved problems associated with Pi. The question of the normality of this number has not been resolved. For example, it is known that Pi and e (the base of the exponent) are transcendental numbers, that is, they are not the roots of any polynomial with integer coefficients. At the same time, however, whether the sum of these two fundamental constants is a transcendental number or not is still unknown.
Moreover, it is still not known whether all numbers from 0 to 9 occur in decimal notation Pi an infinite number of times.
IN in this case ultra-precise calculation of a number is a convenient experiment, the results of which make it possible to formulate hypotheses regarding certain features of the number.
A number is calculated according to certain rules, and during any calculation, in any place and at any time, the same digit appears at a certain place in the number record. This means that there is a certain law according to which a certain number is placed in a certain place in a number. Of course, this law is not simple, but there is still a law. And this means that the numbers in the number are not random, but logical.
Count the number Pi: PI = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ... - 4/n + 4/(n+2)
Pi search or long division:
Pairs of integers that, when divided, give a close approximation to the number Pi. The division was done in a "column" manner to circumvent the length limitations of Visual Basic 6 floating-point numbers.
Pi = 3.14159265358979323846264>33832795028841 971...
Exotic methods of calculating pi, such as using probability theory or prime numbers, also include the method invented by G.A. Galperin, and called Pi-billiard, which is based on the original model. When two balls collide, the smaller of which is between the larger one and the wall, and the larger one moves towards the wall, the number of collisions of the balls makes it possible to calculate Pi with an arbitrarily large predetermined accuracy. You just need to start the process (you can do it on a computer) and count the number of ball hits. The software implementation of this model is not yet known
In every book on entertaining mathematics you will certainly find the history of calculating and clarifying the value of the number "pi". At first, in ancient China, Egypt, Babylon and Greece, fractions were used for calculations, for example, 22/7 or 49/16. In the Middle Ages and the Renaissance, European, Indian and Arab mathematicians refined the value of “pi” to 40 digits after the decimal point, and by the beginning of the Computer Age, through the efforts of many enthusiasts, the number of pi had been increased to 500. This accuracy is purely scientific interest(more on this below), for practice, within the Earth, 11 characters after the dot are enough.
Then, knowing that the radius of the Earth is 6400 km or 6.4 * 1012 millimeters, it turns out that if we discard the twelfth digit of “pi” after the point when calculating the length of the meridian, we will be mistaken by several millimeters. And when calculating the length of the Earth’s orbit when rotating around the Sun (as is known, R = 150 * 106 km = 1.5 * 1014 mm), for the same accuracy it is enough to use “pi” with fourteen digits after the dot. Average distance from the Sun to Pluto, the farthest planet solar system- 40 times the average distance from the Earth to the Sun.
To calculate the length of Pluto's orbit with an error of a few millimeters, sixteen digits of pi are enough. Why bother about trifles - the diameter of our Galaxy is about 100,000 light years (1 light year is approximately equal to 1013 km) or 1018 km or 1030 mm, and in the 27th century 34 pi signs were obtained, which are excessive for such distances.
Why is it difficult to calculate the value of pi? The fact is that not only is it irrational (that is, it cannot be expressed as a fraction P/Q, where P and Q are integers), but it also cannot be a root algebraic equation. A number, for example, an irrational one, cannot be represented by a ratio of integers, but it is the root of the equation X2-2=0, and for the numbers “pi” and e (Euler’s constant), such an algebraic (not differential) equation cannot be specified. Such numbers (transcendental) are calculated by considering a process and are refined by increasing the steps of the process under consideration. The “simplest” way is to inscribe a regular polygon in a circle and calculate the ratio of the perimeter of the polygon to its “radius”...pages marsu
Number explains the world
It seems that two American mathematicians have managed to get closer to solving the mystery of the number pi, which in purely mathematical terms represents the ratio of the circumference of a circle to its diameter, Der Spiegel reports.
As an irrational quantity, it cannot be represented as a complete fraction, so after the decimal point there is an endless series of digits. This property has always attracted mathematicians who sought to find, on the one hand, a more accurate value of pi, and on the other, its generalized formula.
However, mathematicians David Bailey of the Lawrence Berkeley National Laboratory in California and Richard Grendell of Reed College in Portland looked at the number from a different angle - they tried to find some meaning in the seemingly chaotic series of decimal numbers. As a result, it was established that combinations of the following numbers are regularly repeated: 59345 and 78952.
But so far they cannot answer the question of whether the repetition is random or natural. The question of the pattern of repetition of certain combinations of numbers, and not only in the number pi, is one of the most difficult in mathematics. But now we can say something more definite about this number. The discovery paves the way to unraveling the number pi and, in general, to determining its essence - whether it is normal for our world or not.
Both mathematicians have been interested in pi since 1996, and since that time they have had to abandon the so-called “number theory” and turn their attention to “chaos theory,” which is now their main weapon. Researchers construct, based on the display of pi - its most common form is 3.14159... - series of numbers between zero and one - 0.314, 0.141, 0.415, 0.159 and so on. Therefore, if the number pi is truly chaotic, then the series of numbers starting from zero should also be chaotic. But there is no answer to this question yet. The secret of pi, like its older brother - the number 42, with the help of which many researchers are trying to explain the mystery of the universe, has yet to be unraveled."
Interesting data on the distribution of Pi digits.
(Programming is the greatest achievement of humanity. Thanks to it, we regularly learn things that we don’t need to know at all, but are very interesting)
Counted (for a million decimal places):
zeros = 99959,
units = 99758,
twos = 100026,
triples = 100229,
fours = 100230,
fives = 100359,
sixes = 99548,
sevens = 99800,
eight = 99985,
nines = 100106.
In the first 200,000,000,000 decimal places of Pi, the digits occurred with the following frequency:
"0" : 20000030841;
"1" : 19999914711;
"2" : 20000136978;
"3" : 20000069393
"4" : 19999921691;
"5" : 19999917053;
"6" : 19999881515;
"7" : 19999967594
"8" : 20000291044;
"9" : 19999869180;
That is, the numbers are distributed almost evenly. Why? Because according to modern mathematical concepts with an infinite number of digits, there will be exactly the same number of them, in addition, there will be as many ones as there are twos and threes combined, and even as many as all the other nine digits combined. But here you know where to stop, to seize the moment, so to speak, where there are really equal numbers of them.
And one more thing - in the digits of Pi one can expect the appearance of any predetermined sequence of digits. For example, the most common arrangements were found in the following numbers:
01234567891: from 26,852,899,245
01234567891: from 41,952,536,161
01234567891: from 99,972,955,571
01234567891: from 102,081,851,717
01234567891: from 171,257,652,369
01234567890: from 53,217,681,704
27182818284: c 45,111,908,393 are the digits of the number e. (
There was a joke: scientists found the last number in Pi - it turned out to be the number e, they almost got it)
You can search in the first ten thousand digits of Pi for your phone number or date of birth; if that doesn’t work, then look in 100,000 digits.
In the number 1/Pi, starting from 55,172,085,586 digits, there are 33333333333333, isn’t it surprising?
In philosophy, the contingent is usually contrasted with the necessary. So are the signs of pi random? Or are they necessary? Let's say the third digit of pi is "4". And regardless of whoever calculates this pi, in what place and at what time he does it, the third sign will necessarily always be equal to “4”.
The connection between Pi, Phi and the Fibonacci series. The connection between the number 3.1415916 and the number 1.61803 and the Pisa sequence.
- More interesting:
- 1. In the decimal places of Pi, 7, 22, 113, 355 are digit 2. The fractions 22/7 and 355/113 are good approximations to Pi.
- 2. Kokhansky found that Pi is the approximate root of the equation: 9x^4-240x^2+1492=0
- 3. If you write the capital letters of the English alphabet clockwise in a circle and cross out the letters that have symmetry from left to right: A, H, I, M, O, T, U, V, W, X, Y, then the remaining letters form groups according to 3,1,4,1,6 letters.
- (A) BCDEFG (HI) JKL (M) N (O) PQRS (TUVWXY) Z
- 6 3 1 4 1
- So english alphabet must start with the letter H, I or J, not the letter A :)
So what does that matter to us? And it follows from this that in the decimal tail of pi you can find any intended sequence of digits. Your phone? Please, more than once (you can check here, but keep in mind that this page weighs about 300 megabytes, so you will have to wait for the download. You can download a measly million characters here or take my word for it: any sequence of digits in the decimal places of pi is early or it will be late. Any!
For more elevated readers, we can offer another example: if you encrypt all the letters with numbers, then in the decimal expansion of the number pi you can find all the world literature and science, and the recipe for making bechamel sauce, and all the holy books of all religions. I'm not kidding, this is a strict scientific fact. After all, the sequence is INFINITE and the combinations are not repeated, therefore it contains ALL combinations of numbers, and this has already been proven. And if that’s it, then that’s it. Including those that correspond to the book you have chosen.
And this again means that it contains not only all the world literature that has already been written (in particular, those books that burned, etc.), but also all the books that WILL still be written.
It turns out that this number (the only reasonable number in the universe!) rules our world.
The question is how to find them there...
And on this day Albert Einstein was born, who predicted... and what didn’t he predict! ...even dark energy.
This world was shrouded in deep darkness.
Let there be light! And then Newton appeared.
But Satan did not wait long for revenge.
Einstein came and everything became the same as before.
They correlate well - pi and albert...
Theories arise, develop and...
The bottom line: Pi is not equal to 3.14159265358979....
This is a misconception based on the erroneous postulate of identifying flat Euclidean space with the real space of the Universe.
A brief explanation of why in general Pi is not equal to 3.14159265358979...
This phenomenon is associated with the curvature of space. Power lines in the Universe at significant distances there are not ideal straight lines, but slightly curved lines. We have already grown to the point of stating the fact that in real world There are no perfectly straight lines, ideally flat circles, or ideal Euclidean space. Therefore, we must imagine any circle of one radius on a sphere of much larger radius.
We are mistaken in thinking that space is flat, “cubic”. The Universe is not cubic, not cylindrical, and certainly not pyramidal. The universe is spherical. The only case when a plane can be ideal (in the sense of “not curved”) is the case when such a plane passes through the center of the Universe.
Of course, the curvature of a CD-ROM can be neglected, since the diameter of a CD is much smaller than the diameter of the Earth, much less the diameter of the Universe. But we should not neglect the curvature in the orbits of comets and asteroids. The ineradicable Ptolemaic belief that we are still at the center of the Universe can cost us dearly.
Below are the axioms of flat Euclidean (“cubic” Cartesian) space and the additional axiom I formulated for spherical space.
Axioms of flat consciousness:
through 1 point you can draw an infinite number of straight lines and an infinite number of planes.
through 2 points you can draw 1 and only 1 straight line, through which you can draw an infinite number of planes.
In the general case, through 3 points it is impossible to draw a single straight line and one, and only one, plane. Additional axiom for spherical consciousness:
In the general case, through 4 points it is impossible to draw a single straight line, a single plane, and one and only one sphere. Arsentiev Alexey Ivanovich
A little mysticism. Is PI Reasonable?
Any other constant can be defined through the number Pi, including the fine structure constant (alpha), the golden proportion constant (f=1.618...), not to mention the number e - this is why the number pi is found not only in geometry, but also in theory of relativity, quantum mechanics, nuclear physics, etc. Moreover, scientists have recently found that it is through Pi that one can determine the location elementary particles in the Table of Elementary Particles (previously they tried to do this through Woody’s Table), and the message that in the recently deciphered human DNA, the number Pi is responsible for the DNA structure itself (quite complex, it should be noted), produced the effect of a bomb exploding!
According to Dr. Charles Cantor, under whose leadership DNA was deciphered: “It seems that we have come to the solution to some fundamental problem that the universe has thrown at us. The number Pi is everywhere, it controls all the processes known to us, while remaining unchanged! does the number Pi itself control? There is no answer yet."
In fact, Cantor is disingenuous, there is an answer, it’s just so incredible that scientists prefer not to make it public, fearing for own life(more on this a little later): the number Pi controls itself, it is reasonable! Nonsense? Don't rush. After all, Fonvizin also said that “in human ignorance it is very comforting to consider everything as nonsense that you don’t know.”
Firstly, conjectures about the reasonableness of numbers in general have long been visited by many famous mathematicians of our time. Norwegian mathematician Niels Henrik Abel wrote to his mother in February 1829: “I have received confirmation that one of the numbers is reasonable. I spoke with him! But it frightens me that I cannot determine what this number is. But maybe this is for the best. The number warned me that I would be punished if It was revealed." Who knows, Nils would have revealed the meaning of the number that spoke to him, but on March 6, 1829, he passed away.
1955, Japanese Yutaka Taniyama puts forward the hypothesis that “each elliptic curve corresponds to a certain modular form” (as is known, on the basis of this hypothesis Fermat’s theorem was proven). On September 15, 1955, at an international mathematical symposium in Tokyo, where Taniyama announced his hypothesis, in response to a journalist’s question: “How did you come up with this?” - Taniyama replies: “I didn’t think of it, the number told me about it over the phone.” The journalist, thinking that this was a joke, decided to “support” her: “Did it tell you the phone number?” To which Taniyama seriously replied: “It seems that this number has been known to me for a long time, but I can now report it only after three years, 51 days, 15 hours and 30 minutes.” In November 1958, Taniyama committed suicide. Three years, 51 days, 15 hours and 30 minutes is 3.1415. Coincidence? May be. But here's another one, even stranger. The Italian mathematician Sella Quitino also spent several years, as he vaguely put it, “keeping in touch with one cute number.” The figure, according to Quitino, who was already in a psychiatric hospital at that time, “promised to say his name on his birthday.” Could Quitino have lost his mind so much as to call the number Pi a number, or was he deliberately confusing the doctors? It is not clear, but on March 14, 1827, Quitino passed away.
And the most mysterious story is connected with the “great Hardy” (as you all know, this is what contemporaries called the great English mathematician Godfrey Harold Hardy), who, together with his friend John Littlewood, is famous for his work in number theory (especially in the field of Diophantine approximations) and function theory ( where friends became famous for their study of inequalities). As you know, Hardy was officially unmarried, although he repeatedly stated that he was “engaged to the queen of our world.” Fellow scientists more than once heard him talking to someone in his office; no one had ever seen his interlocutor, although his voice was metallic and slightly creaky - for a long time was the talk of the town at Oxford University, where he worked at recent years. In November 1947, these conversations stop, and on December 1, 1947, Hardy is found in a city dump, with a bullet in his stomach. The version of suicide was also confirmed by a note in which Hardy’s hand wrote: “John, you stole the queen from me, I don’t blame you, but I can no longer live without her.”
Is this story related to the number Pi? It’s still unclear, but isn’t it interesting?
Generally speaking, you can collect a lot of similar stories, and, of course, not all of them are tragic.
But, let's move on to "secondly": how can a number even be reasonable? Yes, very simple. Human brain contains 100 billion neurons, the number of pi after the decimal point tends to infinity, in general, according to formal criteria, it can be reasonable. But if you believe the work of the American physicist David Bailey and Canadian mathematicians Peter Borwin and Simon Ploofe, the sequence of decimal places in Pi is subject to chaos theory, roughly speaking, the number Pi is chaos in its original form. Can chaos be intelligent? Certainly! Just like a vacuum, despite its apparent emptiness, as is known, it is by no means empty.
Moreover, if desired, this chaos can be represented graphically - to make sure that it can be reasonable. In 1965, an American mathematician of Polish origin, Stanislaw M. Ulam (he was the one who came up with the key idea for the design of a thermonuclear bomb), while attending one very long and very boring (according to him) meeting, in order to somehow have fun, began to write numbers on checkered paper , included in the number Pi. Putting 3 in the center and moving counterclockwise in a spiral, he wrote out 1, 4, 1, 5, 9, 2, 6, 5 and other numbers after the decimal point. Without any second thought, he simultaneously circled all the prime numbers with black circles. Soon, to his surprise, the circles with amazing tenacity began to line up along straight lines - what happened was very similar to something reasonable. Especially after Ulam generated a color picture based on this drawing using a special algorithm.
Actually, this picture, which can be compared with both the brain and stellar nebula, can be safely called the “brain of Pi”. Approximately with the help of such a structure, this number (the only reasonable number in the universe) controls our world. But how does this control take place? As a rule, with the help of the unwritten laws of physics, chemistry, physiology, astronomy, which are controlled and adjusted by a reasonable number. The above examples show that the intelligent number is also deliberately personified, communicating with scientists as a kind of superpersonality. But if so, did the number Pi come to our world in the guise of an ordinary person?
It's a difficult question. Maybe it came, maybe it didn’t, there is no reliable method for determining this and there cannot be, but if this number is determined by itself in all cases, then we can assume that it came into our world as a person on the day corresponding to its meaning. Of course, the ideal date of birth for Pi is March 14, 1592 (3.141592), however, unfortunately, there are no reliable statistics for this year - we only know that it was in this year, on March 14, that George Villiers Buckingham, the Duke of Buckingham from " The Three Musketeers." He was an excellent fencer, knew a lot about horses and falconry - but was he Pi? Hardly. Duncan MacLeod, born on March 14, 1592, in the mountains of Scotland, could ideally lay claim to the role of the human embodiment of the number Pi - if he were a real person.
But the year (1592) can be determined according to its own, more logical calendar for Pi. If we accept this assumption, then there are many more candidates for the role of Pi.
The most obvious of them is Albert Einstein, born March 14, 1879. But 1879 is 1592 relative to 287 BC! Why exactly 287? Yes, because it was in this year that Archimedes was born, who for the first time in the world calculated the number Pi as the ratio of the circumference to the diameter and proved that it is the same for any circle! Coincidence? But aren’t there a lot of coincidences, don’t you think?
It is not clear in what personality Pi is personified today, but in order to see the meaning of this number for our world, you do not need to be a mathematician: Pi manifests itself in everything that surrounds us. And this, by the way, is very typical for any intelligent being, which, without a doubt, is Pi!
What is a PIN code?
Per-SONAL IDEN-tifi-KA-CI-on number.
What is PI number?
Decoding the number PI (3, 14...) (pin code), anyone can do this without me, through the Glagolitic alphabet. Substitute letters instead of numbers ( numeric values letters are given in Glagolitic) and we get the following phrase: Verbs (verb, say, do) Az (I, as, master, creator) Good. And if we take the following numbers, then it turns out something like this: “I do good, I am Fita (hidden, illegitimate child, virgin birth, unmanifested, 9), I know (I know) distortion (evil) this is speaking (action) will (desire) Earth I do I know I do will good evil (distortion) I know evil I do good..... and so on ad infinitum, there a lot of numbers, but I think it’s all about the same thing...
Music of PI
Studying Pi numbers starts at primary school, when students study the circle, circumference and the value of Pi is encountered. Since the value of Pi is a constant meaning the ratio of the length of the circle itself to the length of the diameter of a given circle. For example, if we take a circle whose diameter is equal to one, then its length is equal to Pi number. This value of Pi is infinite in mathematical continuation, but there is also a generally accepted designation. It comes from a simplified spelling of the value of Pi, it looks like 3.14.
The Historical Birth of Pi
The number Pi supposedly got its roots in Ancient Egypt. Since ancient Egyptian scientists calculated the area of a circle using diameter D, which took the value D - D/92. Which corresponded to 16/92, or 256/81, which means Pi is 3.160.
India in the sixth century BC also touched on the number Pi, in the religion of Jainism, records were found that stated that the number Pi is equal to 10 in the square root, which means 3.162.
Archimedes' teachings on the measurement of the circle in the third century BC led him to the following conclusions:
Later, he substantiated his conclusions by a sequence of calculations using examples of correctly inscribed or described polygonal shapes with doubling the number of sides of these figures. IN accurate calculations Archimedes concluded the ratio of diameter and circumference in numbers between 3 * 10/71 and 3 * 1/7, therefore the value of Pi is 3.1419... Since we have already talked about the infinite shape given value, it looks like 3.1415927... And this is not the limit, because the mathematician Kashi in the fifteenth century calculated the value of Pi as a sixteen-digit value.
English mathematician Johnson W. in 1706, began to use the symbol pi for the symbol? (from Greek it is the first letter in the word circle).
Mysterious meaning.
The value of Pi is irrational and cannot be expressed in fraction form because fractions use whole values. It cannot be a root in the equation, which is why it also turns out to be transcendental; it is found by considering any processes, being refined by large quantity considered steps in this process. There were a lot of attempts to calculate greatest number digits in the number Pi, which led to tens of trillions of digits of a given value from the decimal point.
Interesting fact: Oddly enough, the value of Pi has its own holiday. It is called International Pi Day. It is celebrated on March 14th. The date appeared thanks to the very value of Pi 3.14 (mm.yy) and the physicist Larry Shaw, who was the first to celebrate this holiday in 1987.
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- Pi is the most famous constant in the mathematical world.
- In the Star Trek episode "Wolf in the Shepherd," Spock commands the tinfoil computer to "compute last digit the value of Pi."
- Comedian John Evans once quipped, “What do you get if you divide the circumference of a jack-o-lantern with eye, nose and mouth holes cut into it by its diameter? Pumpkin π!
- Scientists in Carl Sagan's novel "The Connection" tried to unravel the fairly precise value of Pi in order to find hidden messages from the creators of the human race and give people access to "deeper levels of universal knowledge."
- The symbol Pi (π) has been used in mathematical formulas for 250 years.
- During the famous trial of OJ Simpson, a dispute arose between lawyer Robert Blasier and an FBI agent about the actual meaning of Pi. This was all intended to reveal shortcomings in the level of knowledge of a civil service agent.
- Men's cologne from Givenchi, called "Pi", is intended for attractive and forward-thinking people.
- We will never be able to accurately measure the circumference or area of a circle, since we do not know full meaning Pi numbers. This “magic number” is irrational, that is, its numbers are forever changing in a random sequence.
- In the Greek (“π” (piwas)) and English (“p”) alphabets, this symbol is located in position 16.
- In the process of measuring the dimensions of the Great Pyramid of Giza, it turned out that it has the same ratio of height to the perimeter of its base as the radius of a circle to its length, that is, 1/2π
- In mathematics, π is defined as the ratio of the circumference of a circle to its diameter. In other words, π the number of times the diameter of a circle is equal to its perimeter.
- The first 144 decimal places of Pi end with 666, which is referred to in the Bible as the “number of the beast.”
- If we calculate the length of the Earth's equator using the number π, accurate to the ninth decimal place, the error in the calculations will be about 6 mm.
- In 1995, Hiryuki Goto was able to reproduce 42,195 decimal places of Pi from memory, and is still considered the true champion in this field.
- Ludolf van Zeijlen (b. 1540 - d. 1610) spent most of his life calculating the first 36 decimal places of Pi (which were called "Ludolf's digits"). According to legend, these numbers were engraved on his tombstone after his death.
- William Shanks (b.1812-d.1882) worked for many years to find the first 707 digits of Pi. As it turned out later, he made an error in the 527th bit.
- In 2002, a Japanese scientist calculated 1.24 trillion digits in the number Pi using a powerful Hitachi SR 8000 computer. In October 2011, the number π was calculated with an accuracy of 10,000,000,000 decimal places
- Since 360 degrees in full circle and Pi are closely related, some mathematicians were delighted to learn that the numbers 3, 6 and 0 are at the three hundred and fifty-ninth decimal place in Pi.
- One of the first mentions of the number Pi can be found in the texts of an Egyptian scribe named Ahmes (circa 1650 BC), now known as the Ahmes Papyrus (Rinda).
- People have been studying the number pi for 4,000 years.
- The Ahmes papyrus records the first attempt to calculate Pi using the “squaring of the circle,” which involved measuring the diameter of a circle using squares created inside.
- In 1888, a doctor named Edwin Goodwin claimed to have the "supernatural value" of accurately measuring a circle. Soon a bill was proposed in parliament, according to which Edwin could publish copyright on his mathematical results. But this never happened - the bill did not become law, thanks to a mathematics professor in the legislature who proved that Edwin's method led to another incorrect value for Pi.
- The first million decimal places in Pi consist of: 99959 zeros, 99758 ones, 100026 twos, 100229 threes, 100230 fours, 100359 fives, 99548 sixes, 99800 sevens, 99985 eights and 100106 nines.
- Pi Day is celebrated on March 14 (chosen because it is similar to 3.14). The official celebration begins at 1:59 pm in order to comply with 3/14|1:59. Albert Einstein was born on March 3, 1879 (3/14/1879) in Ulm (Kingdom of Württemberg), Germany.
- The meaning of the first numbers in Pi was first correctly calculated by some of the greatest mathematicians ancient world, Archimedes of Syracuse (b.287 - d.212 BC). He represented this number as several fractions. According to legend, Archimedes was so carried away by calculations that he did not notice how the Roman soldiers took it hometown Syracuse. When the Roman soldier approached him, Archimedes shouted in Greek: “Don’t touch my circles!” In response to this, the soldier stabbed him with a sword.
- The exact value of Pi was obtained by Chinese civilization much earlier than Western civilization. The Chinese had two advantages over most other countries in the world: they used a decimal notation and a zero symbol. European mathematicians, on the contrary, did not use the symbolic designation of zero in counting systems until the late Middle Ages, when they came into contact with Indian and Arab mathematicians.
- Al-Khwarizmi (the founder of algebra) worked hard on the calculations of Pi and achieved the first four numbers: 3.1416. The term “algorithm” comes from the name of this great Central Asian scientist, and from his text Kitab al-Jaber wal-Muqabala the word “algebra” appeared.
- Ancient mathematicians tried to calculate Pi, each time entering polygons with a large number sides that fit much more closely into the area of the circle. Archimedes used the 96-gon. Chinese mathematician Liu Hui inscribed the 192-gon, and then the 3072-gon. Tsu Chun and his son managed to fit a polygon with 24576 sides
- William Jones (b.1675–d.1749) introduced the symbol “π” in 1706, which was later popularized in the mathematical community by Leonardo Euler (b.1707–d.1783).
- The Pi symbol "π" came into use in mathematics only in the 1700s, the Arabs invented the decimal system in 1000, and the equal sign "=" appeared in 1557.
- Leonardo da Vinci (b. 1452 – d. 1519) and the artist Albrecht Durer (b. 1471 – d. 1528) had small developments in the “squaring of the circle,” that is, they knew the approximate value of the number Pi.
- Isaac Newton calculated Pi to 16 decimal places.
- Some scientists argue that humans are programmed to find patterns in everything because that is the only way we can make sense of the world and ourselves. And that is why we are so attracted to the “irregular” number Pi))
- Pi may also be referred to as the "circular constant", "Archimedean constant" or "Ludolf number".
- In the seventeenth century, Pi expanded beyond the circle and began to be used in mathematical curves such as the arc and hypocycloid. This happened after the discovery that in these areas some quantities can be expressed through the number Pi itself. In the twentieth century, Pi was already used in many mathematical fields, such as number theory, probability and chaos.
- The first six digits of Pi (314159) are reversed at least six times among the first 10 million decimal places.
- Many mathematicians argue that the correct formulation would be: “a circle is a figure with an infinite number of angles.”
- Thirty-nine decimal places in Pi are enough to calculate the circumference of the circle surrounding known cosmic objects in the Universe, with an error of no more than the radius of a hydrogen atom.
- Plato (b. 427 - d. 348 BC) obtained a fairly accurate value for the number Pi for his time: √ 2 + √ 3 = 3.146.
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