The obvious and the incredible about pi. The number pi - meaning, history, who invented
1. Pi is the most famous constant in the mathematical world.
2. In the Star Trek episode "The Wolf in the Fold," Spock instructs a foil computer to "calculate the value of pi down to the last digit."
3. Comedian John Evans once quipped: “What do you get if you divide the circumference of a pumpkin lantern with cut holes in the shape of an eye, a nose and a mouth by its diameter? Pumpkin pi!
4. The scientists in Carl Sagan's The Connection tried to decipher the fairly accurate meaning of pi to find hidden messages from the creators. human race and give people access to "deeper levels of universal knowledge."
5. Pi symbol (π) is used in mathematical formulas for over 250 years now.
6. During the famous trial of O. J. Simpson, disputes arose between lawyer Robert Blasier and an FBI agent about the actual value of pi. All this was conceived in order to identify shortcomings in the level of knowledge of a civil service agent.
7. Men's cologne from the Givenchy company, called "Pi", is designed for attractive and far-sighted people.
8. We will never be able to accurately measure the circumference or area of a circle, because we do not know full value pi numbers. This "magic number" is irrational, that is, its numbers change forever in a random sequence.
9. In the Greek (“π” (piwas)) and English (“p”) alphabets, this character is located in the 16th position.
10. 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
11. In mathematics, π is defined as the ratio of the circumference of a circle to its diameter. In other words, π is the number of times the circle's diameter is equal to its perimeter.
12. The first 144 digits of pi after the decimal point end with 666, which is referred to in the Bible as "the number of the beast."
14. In 1995, Hiryuki Goto was able to reproduce from memory 42,195 decimal places of pi, and is still considered the real champion in this area.
15. Ludolf van Zeulen (born 1540 - d. 1610) conducted most of his life on the calculations of the first 36 digits after the decimal point of pi (which were called "Ludolf numbers"). According to legend, these figures were engraved on his tombstone after his death.
16. 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 a mistake in bit 527.
17. 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 pi was calculated with an accuracy of 10,000,000,000 decimal places
18. Since 360 degrees in a full circle and the number pi are closely related, some mathematicians were delighted to learn that the numbers 3, 6 and 0 are in the three hundred and fifty-ninth place after the decimal point in the number of pi.
19. One of the first references to the number Pi can be found in the texts of an Egyptian scribe named Ahmes (circa 1650 BC), now known as the papyrus of Ahmes (Rinda).
20. People have been studying the number π for 4,000 years.
21. The Papyrus of Ahmes records the first attempt to calculate Pi from the "square of the circle", which consisted in measuring the diameter of the circle from the squares created inside.
22. In 1888, a doctor named Edwin Goodwin claimed to have "an uncanny value" for the exact measure of a circle. Soon a bill was proposed in Parliament, upon the adoption of which Edwin could publish the copyright for his mathematical results. But that never happened - the bill didn't become law, thanks to a math professor in the legislature who proved that Edwin's method had led to yet another wrong value for pi.
23. The first million decimal places in the number Pi consists of: 99959 zeros, 99758 ones, 100026 twos, 100229 triples, 100230 fours, 100359 fives, 99548 sixes, 99800 sevens, 99985 eights and 100106 nines.
24. Pi Day is celebrated on March 14 (was chosen because of the similarity with 3.14). The official celebration begins at 1:59 pm, in order to fully comply with 3/14|1:59. Albert Einstein was born on March 3, 1879 (3/14/1879) in Ulm (Kingdom of Württemberg), Germany.
25. The value of the first numbers in the number Pi after the first time correctly calculated one of the greatest mathematicians ancient world, Archimedes of Syracuse (b. 287 - d. 212 BC). He represented this number in the form of several fractions. According to legend, Archimedes was so carried away by the calculations that he did not notice how the Roman soldiers took his hometown of Syracuse. When a Roman soldier approached him, Archimedes shouted in Greek, "Don't touch my circles!" In response, the soldier stabbed him with a sword.
26. The exact value of Pi was obtained by Chinese civilization much earlier than Western. The Chinese had two advantages over most of the rest of the world: they used decimal notation and the 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 Arabic mathematicians.
27. Al-Khwarizmi (the founder of algebra) worked hard on the calculations of the number Pi and achieved the first four numbers: 3.1416. The term "algorithm" comes from the name of this great Central Asian scientist, and the word "algebra" appeared from his text Kitab al-Jaber wal-Mukabala.
28. Ancient mathematicians tried to calculate Pi, each time inscribing polygons with a large number of sides, which fit much more closely into the area of a circle. Archimedes used a 96-gon. The Chinese mathematician Liu Hui entered a 192-gon, and then a 3072-gon. Tsu Chong and his son managed to fit a polygon with 24576 sides
29. 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).
30. The pi symbol "π" did not come into use in mathematics until the 1700s, the Arabs invented the decimal system in 1000, and the equal sign "=" appeared in 1557.
31. Leonardo da Vinci (born 1452 - d.1519) and the artist Albrecht Dürer (born 1471 - d.1528) had little experience in "squaring the circle", that is, they had an approximate value of the Pi number.
32. Isaac Newton calculated Pi to 16 decimal places.
33. Some scientists argue that people are programmed to find patterns in everything, because only in this way can they give meaning to the whole world and to themselves. And that is why we are so attracted to the "irregular" number Pi))
34. Pi can also be referred to as the "circular constant", "Archimedean constant" or "Ludolf number".
35. In the seventeenth century, the number pi went beyond the circle and began to be used in mathematical curves, such as the arc and the hypocycloid. This happened after the discovery that in these areas some quantities can be expressed in terms of the Pi number itself. In the twentieth century, pi was already used in many mathematical fields such as number theory, probability, and chaos.
36. The first six digits of pi (314159) are reversed at least six times in the first 10 million decimal places.
37. Many mathematicians argue that the following formulation would be correct: "a circle is a figure with an infinite number of angles."
38. Thirty-nine decimal places in the number Pi is enough to calculate the length of a circle encircling known space objects in the Universe, with an error of no more than the radius of a hydrogen atom.
39. Plato (b. 427 - d. 348 BC) received a fairly accurate value of Pi for his time: √ 2 + √ 3 = 3.146.
The number 3.14 is fundamental to nature, almost magical. Composer David McDonald translated it into piano sheet music and reproduced its sound to 122 decimal places.
The most popular and commonly used constant in the world is PI. Pi is a mathematical constant. It is infinite and means the ratio of the circumference of a circle to the length of its diameter. Approximately pi is equal to 3.14. Pi is not only mathematical concept. It is considered mystical and mysterious.
Here I wanted to recall a few more fun facts about this number.
March 14 is Pi Day. American physicist Larry Shaw in 1987 calculated that exactly on March 14 at 01:59 am the date and time are equal to the first digits of Pi, namely 3.14159. Interestingly, the brilliant physicist Einstein and astronomer Schiaparelli were born on the same day.
The number pi appeared in 1706, and was invented by the scientist William Jones.
The number Pi, as you know, comes from the geometry of the circle. At the same time, it is funny that the number 360 (degrees of a circle) can be seen at the 359th position, after the decimal point in the number Pi.
Both in Greek and Latin alphabet Pi is the sixth letter.
49 decimal places in Pi are enough to calculate the circumference of the universe to within the size of one hydrogen atom.
In the biblical book of kings (7:23) this number is given in the description of the altar of Solomon's Temple
Scientists do not get tired of determining the number of decimal places. So in 2008 their number was 5 trillion, and in 2011 already 10 trillion characters.
Fans of the unique number Pi compete among themselves in who will remember all the numbers after the decimal point more and without errors. On the this moment the record belongs to Chinese guy Liu Chao. In 2006, he spent a day reproducing almost 68,000 decimal places.
In 18888, Dr. Edwin Goodwin of Indiana attempted to file a patent for calculating pi, claiming to have received this knowledge from some celestial agency. Fortunately, the number Pi never became patented thanks to another American professor who found an inaccuracy in his calculations.
Some biologists argue that the human brain is programmed to look for natural combinations of outstanding pi in the ratio, and in fact it is one of the cornerstones of human evolution.
In Seattle, they decided to erect a monument dedicated to the number Pi. Now it rises on the steps of the Museum of Art.
The mystical meaning of Pi appears when you add up the first 144 decimal places. It turns out the "number of the beast" is 666.
In the UK in 2008, the fields suddenly appeared mysterious circles. Scientists saw a pattern in them. Surprisingly, the first ten digits of Pi were encrypted in circles.
The number Pi is also called the Ludolf number in honor of Ludolf van Zeulen. This is a scientist who devoted his life to calculating and researching the first 36 digits of a number. The tombstone on the grave of the scientist with these engraved figures mysteriously disappeared.
For intellectual and attractive men fashion house Givenchy has launched a cologne under the laconic name "Pi"
About how calculating all the signs of pi can lead to madness, in 1998, the film Pi: Faith in Chaos was shot by director Darren Anofsky.
Everyone came across the number Pi in mathematics lessons at school, but few people know how interesting, mysterious and even mystical it is. The maximum that was deposited in mass consciousness for the average student is that it is the result of dividing the length of any circle by its own diameter. In fact, for thousands of years people have been trying to understand its essence and strength, using it in both the simplest and most complex mathematical calculations. In the era of antiquity, it interested a person from the standpoint of geometry, in the Middle Ages it was actively used in the development mathematical analysis, it has not lost its importance in the era of digital computers.
What kind Interesting Facts and secrets hides in itself this number?
It is absolutely infinite and irrational, since the sequence of numbers that compose it has no end and does not repeat with any periodicity. Therefore, there is no absolutely exact final value of π. In fact, this is an expression of chaos, its digital record.
It was not the same at all times and not among all peoples; serious errors were made in determining its meaning. For example, the ancient Egyptians considered Pi equal to 3.1604, and the ancient Hindus - 3.162. The closest to the truth at that time were the Chinese, who took its value of 3.1459. According to experts, it was this error, and not at all God's wrath and confusion of languages, that caused failures in the construction of the biblical Tower of Babel.
There is a special Pi-club in the world, organized by mathematicians different countries. It is not so easy to become a member, for this you need to have not only outstanding mathematical thinking, but also an excellent memory. Memorizing as long as possible the sequence of digits of the pi constant is the entrance ticket to this elite club.
There are many techniques for memorizing the numerical sequence after the decimal point. These are specially composed texts, and even verses in which each subsequent word has the required number of letters, and a breakdown into groups with a certain association, and other convenient structuring. The record in this direction today belongs to the Japanese Haraguchi, who was able to reproduce 83,000 digits in memory.
His record could easily be broken by a Chinese resident named Liu Chao, who memorized 93 thousand, if he had not made an unfortunate mistake at 67890 sign. It is known that it took him exactly a day and another 4 minutes without breaks for food, sleep and toilet, which is all the more offensive.
In the holiday calendar, there are two dates for celebrating the number of Pi. The first one, as expected, echoes itself and is celebrated on March 14, forming the initial value of the number (3.14). Mathematicians and other scientists in the field exact sciences, of course, do not miss this day, celebrating it cheerfully and creatively. For a holiday all over the world, it is customary to cook all kinds of goodies with the image of the “birthday man” or in his form. After the tasting, fun and, of course, smart quizzes are held. By the way, on this day Albert Einstein was born and Stephen Hawking died.
The second date is related to the European calendar entry format and is celebrated on July 22 (22/7). It is known that the value of this fraction is an approximate value of the famous constant.
The Bank of Russia issued a coin in denomination of "Pi" rubles dedicated to the date. Among numismatists, of course, it is valued much more than 3 rubles 14 kopecks.
The first mention of the number π is found on a papyrus in the mathematical calculations of Ahmes in 1650 BC. Now an ancient scroll with attempts to calculate the constant by "squaring the circle." It contains the measurement of the area of a circle by inscribing many squares into it.
Several sequences of numbers in a common chain have their own name. For example, it contains six nines in a row at once, named after the US physicist Richard Feynman. In one scientific community he expressed the idea that he would like to learn the sequence up to this point in order to pronounce or write down the number “9” six times in the end, which would sound like entering a period, and therefore the rationality of the number. Alas, the sixth nine (the Feiman point) is followed by the eight, and the irrational infinity continues.
Ancient mathematicians tried to calculate the circumference and area of a circle by inscribing polygons (a geometric equilateral polygon) into it, the perimeter of which was calculated based on the number of angles. The more there were, the more accurate the result was. It is known that Archimedes used a 96-gon in his calculations. He was easily overtaken by the Chinese Liu Hui, who managed to inscribe a 192-coal polygon in the outlined circle, and then a 3072-coal one. It was his calculation that remained the most accurate in the next millennium.
To date, computers have calculated the number Pi with a sequence of digits of 13.3 trillion digits. While this is the limit. Further calculations require quantum computers with even higher power and speed.
It is proved that the famous Egyptian pyramid in Giza is an architectural embodiment of the value of the constant π. The ratio of its height to the sum of the sides of the base (perimeter) exactly repeats this number (the golden ratio).
The sequence of the first 6 digits occurs in the first chain of 10 million. characters 6 times, but in reverse order.
If we calculate the length of the earth's equator using the Pi number, then the error will be only 6 mm.
At the beginning of the new century in Great Britain, circles appeared in its mysterious fields, known as places of power, which were carefully studied by scientists. They managed to decipher a sequence of 10 digits that exactly repeated the beginning of the number π.
In the early 200s, an enterprising Indian took over a domain name of the maximum allowed 63 characters, in which he repeated the constant sequence. Subsequently, he successfully sold it to the German mathematician Steffens. On his website, he posted a proposal to calculate or randomly find a page that displays a million decimal places of pi. At the same time, a link to this page it was impossible to find.
Another site with the domain name pi.com has nothing but a sequence of pi. You can contact the owner only by transferring $ 3 according to the specified data.
The famous number was also noted in art. In 1998, Pi: Faith in Chaos was released. Main character tried to find simple answers to mysterious things, in particular, the “key number” that underlies all natural patterns, as a result of which he went crazy. Darren Aronofoska, who directed the film, was awarded Best Director at the Sundance Film Festival.
Scientists, who decided to simplify the mysterious number and the formulas associated with it, introduced an alternative constant, tau, where the diameter of a circle is replaced by its radius. The day of the opponent is proposed, according to calculations, to be celebrated on June 28. By the way, English phrase“I prefer pi” is read the same from the beginning and from the end (I prefer pi).
The calculation of the Pi constant is standard for testing the computing power of the next computer device, this is its so-called "digital cardiogram".
In mirror image, the first three digits resemble English word pie PIE, which is pronounced exactly the same -.
This is just a part amazing facts about the number Pi, accessible for understanding to a simple layman far from science. As for mathematical minds, for them the mystical constant opens up truly incredible horizons for research, discoveries and amazing coincidences, which, perhaps someday, will reveal their mysterious laws to them.
abstract
The amazing number pi
Introduction
March is Pi Day around the world. This holiday was invented in 1987 by San Francisco physicist Larry Shaw, who noticed that in American system date entries (month/day) date March 14 (3.14) and time 1:59 coincides with the first digits of the day π = 3.14159). Pi Day is usually celebrated at 1:59 pm local time (12-hour clock). By the holiday they bake (or buy) pies (cakes), because in English π pronounced like "pie", which sounds the same as the word pie ("pie"). Special celebrations take place in scientific societies and educational institutions. Interestingly, the Pi holiday, celebrated on March 14, coincides with the birthday of one of the most prominent physicists of our time, Albert Einstein. We are interested in this number. Who first guessed about the relationship between the circumference of a circle and its diameter? Who was the first to calculate its value? What is the history of this number? Why is this number called π»?
Purpose of the work: to get acquainted with the number π, study the history of its discovery methods of finding study the history of the discovery of the number π;
Learn how to find a number π;
To conclude. 1. Number designationπ
We know who built the first plane, who invented the radio, but no one knows who was the first to guess about the relationship between the circumference and its diameter. But it is known when the first designation of a given number with a letter appeared. It is believed that for the first time this designation was introduced by the English teacher William Johnson (1675-1749) in his work "Review of the achievements of mathematics", published in 1706. Even earlier, in 1647, the English mathematician Outred used the letter π to indicate the circumference of a circle. It is assumed that this designation was prompted by the first letter of the Greek alphabet of the word περιφερια - circle. But the international standard designation π for the number 3, 141592 ... became after it was applied by the famous Russian academician, mathematician Leonhard Euler in his works in 1737. He wrote: "There are many other ways of finding the lengths or areas of the corresponding curve or flat figure which can make the practice much easier. . Number historyπ
It is believed that the number π was first discovered by the Babylonian Magi. It was used in the construction of the famous Tower of Babel, whose history is included in the Bible. However, insufficiently accurate calculation led to the collapse of the entire project. It is also believed that the number Pi underlay the construction of the famous Temple of King Solomon. History of numbers π proceeded in parallel with the development of all mathematics. Some authors divide the whole process into 3 periods: ancient period, during which π studied from the position of geometry, the classical era that followed the development of mathematical analysis in Europe in the 17th century, and the era of digital computers. ancient period Any schoolboy now calculates the circumference of a circle by diameter much more accurately than the wisest priest ancient country pyramids or the most skillful architect of the great Rome. In ancient times, it was believed that the circumference is exactly 3 times longer than the diameter. This information is contained in the cuneiform tablets of the Ancient Interfluve. The same meaning can be seen in the text of the Bible: “And he made a sea of cast copper, - from its edge to edge ten cubits, - completely round ... and a string of thirty cubits hugged it around.” However, already in the II millennium BC. mathematics ancient egypt found a more accurate relationship. In the Rhind Papyrus, which dates back to about 1650 B.C. for number π the value (16/9) 2 is given, which is approximately 3.16. The ancient Romans believed that the circumference is longer than the diameter of 3.12, while the correct ratio is 3.14159 ... Egyptian and Roman mathematicians did not establish the ratio of the circumference to the diameter by strict geometric calculation, like later mathematicians, but found it simply from experience. But why did they make such mistakes? Couldn't they wrap a thread around some round thing and then, straightening the thread, just measure it? Take, for example, a vase with a round bottom and a diameter of 100 mm. The circumference should be 314 mm. However, in practice, measuring with a thread, we will hardly get this length: it is easy to make a mistake by one millimeter, and then π will be equal to 3.13 or 3.15. And if we take into account that the diameter of the vase cannot be measured quite accurately, that here, too, an error of 1 mm is very likely, then for π rather wide limits between 3.09 and 3.18 are obtained. We decided to conduct some experiments. For this, several circles were drawn. With the help of a thread and a ruler, we measured the length of each circle and its diameter. Then divide the circumference by its diameter. We got the following results. No. CircumferenceDiameter π 114.5 cm5 cm2.9231 cm10 cm3.1310 cm3 cm3, (3)419.5 cm6.5 cm3516.5 cm5 cm3.5618 cm6 cm3735 cm11 cm3, (18)820.5 cm6.5 cm3.15922 cm6.9 cm3.191021 cm3 cm31113 cm4 cm3.25126 cm1.7 cm3.51312 cm4 cm31412.5 cm4 cm3, 1251526 cm8 cm3.251638 cm12 cm3.2 mathematical pi number digit Average value - 3.168 Defining π in this way, you can get a result that does not coincide with 3.14: once we get 3.1, another time 3.12, the third time 3.17, etc. By chance, 3.14 may be among them, but in the eyes of the calculator this number will not have more weight than others. This kind of empirical path cannot in any way give any acceptable value for π. In this regard, it becomes more understandable why the ancient world did not know the correct ratio of circumference to diameter. From the 4th century BC mathematical science developed rapidly in Ancient Greece. The ancient Greek geometers strictly proved that the circumference of a circle is proportional to its diameter, and the area of a circle is equal to half the product of the circumference and the radius S = ½ C R = π R2 . This proof is attributed to Euclid of Cnidus and Archimedes. Archimedes in his essay “On the Measurement of a Circle” calculated the perimeters of inscribed in a circle and described around it regular polygons- from 6 - to 96-gon. Taking the diameter of a circle as unity, Archimedes considered the perimeter of an inscribed polygon as a lower bound for the circumference of a circle, and the perimeter of an inscribed polygon as an upper bound. Considering a regular 96-gon, Archimedes received the estimate Thus, he established that the number π concluded within 3,1408 < π < 3,1428. The value 22/7 is still considered quite a good approximation of the number π for applied tasks. In the "Algebra" of the ancient Arab mathematician Mohammed ben Muz, we read the following lines about calculating the circumference of a circle: "The best way is to multiply the diameter by 3 1/7. This is the fastest and easiest way. God knows the best." Zhang Heng clarified the meaning of the number in the 2nd century π, offering two of its equivalents: 1) 92/29 ≈ 3.1724…, 2) √10. In India, Aryabhata and Bhaskara used an approximation of 3.1416. Brahmagupta in the 7th century suggested √10 as an approximation. Around 265 AD mathematician Liu Hui from the kingdom of Wei provided a simple and precise algorithm for calculating π with any degree of accuracy. He independently carried out the calculation for the 3072-gon and obtained an approximate value for π, π ≈3,14159.
Later, Liu Hui came up with fast method calculations π and came up with an approximate value of 3.1416 with just a 96-gon, taking advantage of the fact that the difference in area of successive polygons forms geometric progression with denominator 4. In the 480s, the Chinese mathematician Zu Chongzhi demonstrated that π ≈355/113, and showed that 3.1415926< π < 3,1415927, using Liu Hui's algorithm applied to a 12288-gon. This value remained the most accurate approximation of the number π over the next 900 years. Until the II millennium, no more than 10 digits were known π.
classical period Further major advances in learning π associated with the development of mathematical analysis, in particular with the discovery of series that make it possible to calculate π with any precision, summing up a suitable number of terms of the series. In the 1400s, Madhava of Sangamagrama found the first such series. This result is known as the Madhava-Leibniz or Gregory-Leibniz series (after it was rediscovered by James Gregory and Gottfried Leibniz in the 17th century). However, this series converges to π very slowly, which leads to the difficulty of calculating the many digits of a number in practice - it is necessary to add about 4000 terms of the series to improve Archimedes' estimate. However, by converting this series to Madhava was able to calculate π as 3.14159265359, correctly identifying 11 digits in the number entry. This record was broken in 1424 by the Persian mathematician Jamshid al-Kashi, who in his work entitled "Treatise on the Circle" gave 17 digits of the number π, of which 16 are correct. The first major European contribution since Archimedes was that of the Dutch mathematician Ludolf van Zeulen, who spent ten years calculating the number π with 20 decimal digits (this result was published in 1596). Applying the method of Archimedes, he brought doubling to an n-gon, where n = 60 229. Having outlined his results in the essay “On the Circumference” (“Van den Circkel”), Ludolf ended it with the words: “Whoever has a desire, let him go further.” After his death, 15 more exact digits of the number were found in his manuscripts. π. Ludolph bequeathed that the signs he found were carved on his tombstone. number in his honor π sometimes called the "Ludolf number", or the "Ludolf constant". Around this time, methods for analyzing and defining infinite series began to develop in Europe. The first such representation was Vieta's formula, found by François Vieta in 1593. Others famous result became the Wallis formula: derived by John Wallis in 1655. The Leibniz series, first found by Madhava from the Sangamagram in 1400 In modern times for calculation π analytical methods based on identities are used. Euler, author of the notation π, received 153 correct signs. The best result for late XIX century was obtained by the Englishman William Shanks, who took 15 years to calculate 707 digits, although due to an error only the first 527 were correct. To avoid such errors, modern calculations of this kind are carried out twice. If the results match, then they are likely to be correct. The era of digital computers Shanks' bug was discovered by one of the first computers in 1948; he counted 808 characters in a few hours π.
With the advent of computers, the pace has increased: year - 2037 decimal places (John von Neumann, ENIAC), year - 10000 decimal places (F. Zhenyuy, IBM-704), year - 100000 decimal places (D. Shanks, IBM-7090), year - 10,000,000 decimal places (J. Guillou, M. Bouillet, CDC-7600), year - 29360000 decimal places (D. Bailey, Cray-2), year - 134217000 decimal places (T. Canada, NEC SX2), year - 1011196691 decimal places (D. Chudnovsky and G. Chudnovsky, Cray-2+IBM-3040). They also achieved 2260000000 characters in 1991, and 4044000000 characters in 1994. Further records belong to the Japanese Tamura Canada: in 1995, 4294967286 characters, in 1997 - 51539600000. By 2011, scientists were able to calculate the value of the number π with an accuracy of 10 trillion decimal places! 3. Poetry of numbersπ
Let us carefully consider its first thousand characters, let us be imbued with the poetry of these numbers, because behind them are the shadows of the greatest thinkers of the Ancient World and the Middle Ages, the New and the present. 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 Interesting data about the distribution of digits of a number π. Someone was not too lazy, counted (for a million digits after the decimal point): zeros - 99959, units -99758, deuces -100026, triplets - 100229, fours - 100230, fives - 100359, sixes - 99548, sevens - 99800, eights - 99985, nines -100106. Digits of the decimal representation of a number π quite random. It contains any sequence of numbers, you just need to find it. In this number, all written and unwritten books are present in coded form, any information that can be invented is already embedded in π. You just need to consider more signs, find the right area and decipher it. Here everyone can find their phone number, their date of birth or their home address. Since there are no repetitions in the sequence of signs of pi, this means that the sequence of signs of pi obeys chaos theory, 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 reasonable. In 1965, the American mathematician M. Ulam, sitting at a boring meeting, from nothing to do, began to write numbers included in the number pi on checkered paper. Putting 3 in the center and moving in a counterclockwise spiral, he wrote out 1, 4, 1, 5, 9, 2, 6, 5 and other numbers after the decimal point. Along the way, he circled all prime numbers circles. What was his surprise and horror when the circles began to line up along the straight lines! Later, he generated a color picture based on this drawing using a special algorithm. Long numbers that approximate a value π, have neither practical nor theoretical value. If we wanted, for example, to calculate the length of the earth's equator with an accuracy of 1 cm, assuming that the loan is the length of its diameter exactly, then for this it would be quite enough for us to take only 9 digits after the decimal point in the number π. And taking twice as many numbers (18), we could calculate the length of a circle with a radius of the distance from the Earth to the Sun, with an error of no more than 0.0001 mm (100 times less than the thickness of a hair!). For ordinary calculations with a number π it is quite enough to fill in two decimal places (3.14), and for more accurate ones - four decimal places (3.1416: we take the last digit 6 instead of 5 because the number that follows is greater than 5). Mnemonists love to memorize numbers π. And they compete in the number of memorized digits of this infinite number. Record holders from different countries are listed in the book of records. So the Japanese Hideaki Tomoyori can reproduce the number of pi up to 40,000 characters. It took him about 10 years to memorize such a number of digits. Russian record in memorizing the number PI is much more modest. Alexander Belyaev reproduced 2500 digits of the number PI. It took him an hour and a half to remember the numbers. For memorization - a month and a half. The record for memorizing the number Pi belongs to the Ukrainian Andrey Slyusarchuk, who memorized 30 million decimal places. Since a simple enumeration of this would take a whole year, the judges checked Slyusarchuk in the following way - they asked him to name arbitrary sequences of the number Pi from any of the 30 million signs. The answer was checked against a 20-volume printout. Mnemonists memorize a number π for one simple reason. If they reproduced just a series of random numbers, then suspicions might arise that a person did not remember these numbers, but reproduces them according to some system. But when a person reproduces an infinite number π, then any suspicions of dishonesty disappear, since there is no pattern in the sequence of numbers in the number π no. And the only way to reproduce these numbers is to memorize them. Small poems or vivid phrases remain in memory longer than numbers, so to remember any numerical value π come up with special poems or individual phrases. In the works of this type of "mathematical poetry" words are selected so that the number of letters in each word consistently matches the corresponding digit of the number π. A famous poem English language- in 13 words, therefore giving 12 decimal places in the number π
See I have a rhyme assistingfeeble brain, its tasks off times resisting; on the German- in 24 words, and on French in 30 words. They are curious, but too large, heavy. There are such verses and sentences in Russian. For example, "This I know and remember perfectly." "And many signs are superfluous to me, in vain." "What do I know about circles?" - a question that implicitly contains the answer: 3.1416. “Learn and know in the number known behind the number the number, how good luck, note” (= 3.14159265358). Archimedean number "Twenty-two owls were bored On big dry bitches. Twenty-two owls dreamed About the seven big mice. "You just have to try And remember everything as it is: Three, fourteen, fifteen Ninety-two and six. There is a monument to the number in the world π - it is installed in Seattle in front of the Museum of Art. There are also Pi-clubs, whose members, being fans of the mysterious mathematical phenomenon, collect all the new information about the number Pi and try to unravel its mystery. In 2005, singer Kate Bush released the album Aerial, which included a song about the number π. In the song, which the singer called “Pi”, 124 numbers from the famous number series sounded. But in her song, the 25th number of the sequence is incorrectly named, and as many as 22 numbers have disappeared somewhere. Conclusion
While working on the abstract, we learned a lot of new and interesting things about the number π.
Number π has occupied the minds of scientists from ancient times to the present day. But it is not known who was the first to guess about the relationship between the circumference and its diameter. international standard designation π for the number 3, 141592 became after it was applied by the famous Russian academician, mathematician Leonard Euler in his works in 1737. Number history π can be divided into 3 periods: the ancient period, the classical era and the era of digital computers. Various methods were used to calculate it. Number π also called the "Ludolf number". Number π infinite non-periodic fraction. The digits of its decimal representation are quite random. No other number is as mysterious as "Pi" with its famous never-ending series of numbers. In many areas of mathematics and physics, scientists use this number and its laws. Some scholars even consider him one of the five the most important numbers in mathematics. Number π many admirers not only among scientists. Exist Pi - clubs of fans of this number, many sites on the Internet are dedicated to this amazing number. “Wherever we turn our eyes, we see a nimble and industrious number: it is contained in the simplest wheel, and in the most complex automatic machine.” Kympan F. List of sources used
1.Zhukov A.V. "The ubiquitous number π». - M: Editorial URSS, 2004, - 216s
The number Pi is the most famous constant in the mathematical world and is equal to 3.1415926535…
In the Star Trek episode "The Wolf in the Fold", Spock instructs a foil computer to "calculate the value of pi down to the last digit".
Comedian John Evans once quipped, “What do you get if you divide the circumference of a gourd lantern with eye, nose, and mouth holes cut into it by its diameter? Pumpkin pi!
The scientists in Carl Sagan's novel The Connection tried to decipher the fairly accurate meaning of pi in order to find hidden messages from the creators of the human race and open people access to "deeper levels of universal knowledge."
The symbol Pi (π) has been used in mathematical formulas for over 250 years.
During the famous trial of OJ Simpson, lawyer Robert Blasier and an FBI agent argued over the actual meaning of pi. All this was conceived in order to identify shortcomings in the level of knowledge of a civil service agent.
Men's cologne from the Givenchy company, called "Pi", is designed for attractive and far-sighted people.
We will never be able to accurately measure the circumference or area of a circle, because we do not know the full value of Pi. This "magic number" is irrational, that is, its numbers change forever in a random sequence.
In the Greek ("π" (piwas)) and English ("p") alphabets, this character is located in the 16th position.
In the process of measuring the dimensions of the Great Pyramid at Giza, it turned out that it has the same ratio of height to the perimeter of its base as the radius of a circle to its length, that is, 1/2π
In mathematics, π is defined as the ratio of the circumference of a circle to its diameter. In other words, π is the number of times the circle's diameter is equal to its perimeter.
The first 144 digits of pi after the decimal point end with 666, which is referred to in the Bible as the "number of the beast".
In 1995, Hiryuki Goto was able to reproduce 42,195 decimal places of pi from memory, and is still considered the real champion in this area.
Ludolf van Zeulen (born 1540 - d. 1610) spent most of his life calculating the first 36 digits after the decimal point of pi (which were called "Ludolf digits"). According to legend, these figures 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 a mistake in bit 527.
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 pi was calculated with an accuracy of 10,000,000,000,000 decimal places
Since 360 degrees in a full circle and pi are closely related, some mathematicians were delighted to learn that the numbers 3, 6, and 0 are in the three hundred and fifty-ninth decimal place in the number of pi.
One of the first references to the number Pi can be found in the texts of an Egyptian scribe named Ahmes (circa 1650 BC), now known as the Papyrus of Ahmes (Rinda).
People have been studying the number pi for 4,000 years.
The Ahmes papyrus records the first attempt to calculate pi from the "square of the circle", which consisted of measuring the diameter of the circle from the squares created inside.
In 1888, a doctor named Edwin Goodwin claimed to have "an uncanny value" for the exact measure of a circle. Soon a bill was proposed in Parliament, upon the adoption of which Edwin could publish the copyright for his mathematical results. But that never happened - the bill didn't become law, thanks to a math professor in the legislature who proved that Edwin's method had led to yet another wrong value for pi.
The first million digits after the decimal point in the number Pi consists of: 99959 zeros, 99758 ones, 100026 twos, 100229 triplets, 100230 fours, 100359 fives, 99548 sixes, 99800 sevens, 99985 eights and 100106 nines.
Pi Day is celebrated on March 14 (it was chosen due to its similarity with 3.14). The official celebration begins at 1:59 pm, in order to fully comply with 3/14|1:59.
The value of the first numbers in the number Pi after was first correctly calculated by one of the greatest mathematicians of the ancient world, Archimedes of Syracuse (b.287 - d.212 BC). He represented this number in the form of several fractions. According to legend, Archimedes was so carried away by the calculations that he did not notice how the Roman soldiers took his hometown of Syracuse. When a Roman soldier approached him, Archimedes shouted in Greek, "Don't touch my circles!" In response, the soldier stabbed him with a sword.
The exact value of Pi was obtained by Chinese civilization much earlier than Western. The Chinese had two advantages over most of the rest of the world: they used decimal notation and the 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 Arabic 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 the word "algebra" appeared from his text Kitab al-Jaber wal-Mukabala.
Ancient mathematicians tried to calculate pi, each time inscribing polygons with a large number of sides, which fit much more closely into the area of a circle. Archimedes used a 96-gon. The Chinese mathematician Liu Hui entered a 192-gon, and then a 3072-gon. Tsu Chong 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" did not come into use in mathematics until the 1700s, the Arabs invented the decimal system in 1000, and the equal sign "=" appeared in 1557.
Leonardo da Vinci (born 1452 - d. 1519) and the artist Albrecht Dürer (born 1471 - d. 1528) had little experience in "squaring the circle", that is, they had an approximate value for the Pi number.
Isaac Newton calculated pi to 16 decimal places.
Some scientists argue that people are programmed to find patterns in everything, because only in this way can they give meaning to the whole world and to themselves. 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 moved beyond the circle and began to be used in mathematical curves such as the arc and the hypocycloid. This happened after the discovery that in these areas some quantities can be expressed in terms of the Pi number 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 in the first 10 million decimal places.
Many mathematicians argue that the following formulation will be correct: "a circle is a figure with an infinite number of angles."
Thirty-nine decimal places in the number Pi is enough to calculate the circumference of the known space objects in the Universe, with an error of no more than the radius of a hydrogen atom.
Plato (b. 427 - d. 348 BC) received a fairly accurate value of pi for his time: √ 2 + √ 3 = 3.146.
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