The history of the origin of the number pi interesting facts. Interesting facts about the number pi. Pi calculations

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 when you divide the circumference of a pumpkin 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 unravel the fairly accurate meaning of pi in order to find hidden messages from the creators. human race and give people access to "deeper levels of universal knowledge."

Pi symbol (π) is used in mathematical formulas for over 250 years now.

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 dimensions 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 decimal digits 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 this never happened - the bill did not become law, thanks to a professor of mathematics in legislature, who proved that Edwin's method led to another incorrect value of pi.

The first one million decimal places in 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 the first time correctly calculated by 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 it hometown Syracuse. When a Roman soldier approached him, Archimedes shouted in Greek, "Don't touch my circles!" In response, the soldier stabbed him with his 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 digits after the decimal point in the number Pi is enough to calculate the circumference of a circle encircling 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.

For many centuries and even, oddly enough, millennia, people have understood the importance and value for science of the mathematical constant, equal to the ratio the circumference of a circle to its diameter. the number pi is still unknown, but the best mathematicians throughout our history have been related to it. Most of them wanted to express it as a rational number.

1. Researchers and true fans of the number Pi have organized a club, for entry into which you need to know enough by heart a large number of his signs.

2. Pi Day has been celebrated since 1988 and falls on March 14th. Prepare salads, cakes, cookies, pastries with his image.

3. Pi has already been set to music, and it sounds pretty good. He was even erected a monument in Seattle, American, in front of the City Museum of Art.

At that distant time, they tried to calculate the number Pi using geometry. The fact that this number is constant for a variety of circles was known even by geometers in Ancient Egypt, Babylon, India and Ancient Greece, who claimed in their works that it is only a little more than three.

In one of the sacred books of Jainism (an ancient Indian religion that originated in the 6th century BC), it is mentioned that then the number Pi was considered equal to the square root of ten, which ultimately gives 3.162 ....

Ancient Greek mathematicians measured a circle by constructing a segment, but in order to measure a circle, they had to build an equal square, that is, a figure equal to it in area.

When you didn't know decimal fractions, the great Archimedes found the value of Pi with an accuracy of 99.9%. He discovered a method that became the basis of many subsequent calculations, inscribed in a circle and described regular polygons around it. As a result, Archimedes calculated the value of Pi as the ratio 22/7 ≈ 3.142857142857143.

In China, mathematician and court astronomer, Zu Chongzhi in the 5th century BC. e. designated a more accurate value of the number Pi, calculating it to seven digits after the decimal point and determined its value between the numbers 3, 1415926 and 3.1415927. It took more than 900 years for scientists to continue this digital series.

Middle Ages

The famous Indian scientist Madhava, who lived at the turn of the XIV - XV centuries, who became the founder of the Kerala school of astronomy and mathematics, for the first time in history began to work on the decomposition trigonometric functions into the ranks. True, only two of his works have survived, while others are known only for references and quotations from his students. In the scientific treatise "Mahajyanayana", which is attributed to Madhava, it is indicated that the number Pi is 3.14159265359. And in the treatise "Sadratnamala" there is a number with even more exact decimal places: 3.14159265358979324. In the indicated numbers, the last digits do not correspond to the correct value.

In the 15th century, the Samarkand mathematician and astronomer Al-Kashi calculated the number Pi with sixteen decimal places. His result was considered the most accurate for the next 250 years.

W. Johnson, a mathematician from England, was one of the first to designate the ratio of the circumference of a circle to its diameter with the letter π. Pi is the first letter of the Greek word "περιφέρεια" - circle. But this designation managed to become generally accepted only after it was used in 1736 by the more famous scientist L. Euler.

Conclusion

Modern scientists continue to work on further calculations of the values of pi. For this, supercomputers are already being used. In 2011, a scientist from Shigeru Kondo, collaborating with American student Alexander Yi, correctly calculated a sequence of 10 trillion digits. But it is still unclear who discovered the number Pi, who first thought about this problem and made the first calculations of this truly mystical number.

On March 14, a very unusual holiday is celebrated all over the world - Pi Day. Everyone has known it since school days. Students are immediately explained that the number Pi is a mathematical constant, the ratio of the circumference of a circle to its diameter, which has an infinite value. It turns out that a lot of interesting facts are connected with this number.

Monument to Pi in Seattle, USA, on the steps in front of the Museum of Art, the only monument to this remarkable number.

1. The history of number has more than one millennium, almost as long as the science of mathematics exists. Of course, the exact value of the number was not immediately calculated. At first, the ratio of the circumference to the 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 the initial letters of two Greek words meaning "circumference" and "perimeter". The mathematician Jones endowed the number with the letter "π", and she firmly entered mathematics already in 1737.

2. In different eras and among different peoples, the number Pi had different meaning. For example, in ancient Egypt it was 3.1604, among the Hindus it acquired the value of 3.162, the Chinese used the number equal to 3.1459. Over time, π was calculated more and more accurately, and when computer technology appeared, that is, a computer, it began to have more than 4 billion characters.

3. There is a legend, more precisely, 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 mistaken. A similar version exists regarding Solomon's temple.

4. It is noteworthy that they tried to introduce the value of Pi even at the state level, that is, through the law. In 1897, a bill was drafted in the state of Indiana. Pi was 3.2 according to the document. However, scientists intervened in time and thus prevented an error. In particular, Professor Purdue, who was present at the legislative assembly, spoke out against the bill.

5. It is interesting that several numbers in the infinite sequence Pi have their own name. So, six nines of Pi are named after the American physicist Feynman. Once Richard Feynman was giving a lecture and stunned the audience with a remark. He said he wanted to learn the digits of pi up to six nines by heart, only to say "nine" six times at the end of the story, hinting that its meaning was rational. When in fact it is irrational.

Feynman point.

6. Mathematicians around the world do not stop doing research related to the number Pi. It is literally shrouded in mystery. Some theorists even believe that it contains a universal truth. In order to share knowledge and new information about Pi, they organized the Pi Club. Entering it is not easy, you need to have an outstanding memory. So, those wishing to become a member of the club are examined: a person must tell as many signs of the number Pi from memory as possible.

7. They even came up with various techniques for remembering the number Pi after the decimal point. For example, they come up with whole texts. In them, words have the same number of letters as the corresponding digit after the decimal point. To further simplify the memorization of such a long number, they compose verses 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 ingenuity. 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) 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 was able to memorize only two and a half thousand numbers after the decimal point of Pi.

"Pi" in perspective.

9. Pi Day has been celebrated for more than a quarter of a century, since 1988. Once, a physicist from the Popular Science Museum in San Francisco, Larry Shaw, noticed that March 14 was spelled the same as pi. In a date, the month and day form 3.14.

10. Pi Day is celebrated not only in an original way, but in a fun way. Of course, scientists who occupy exact sciences. For them, this is a way not to break away from what they love, but at the same time to relax. On this day, people gather and cook different goodies with the image of Pi. Especially there is a place for confectioners to roam. They can make pi cakes and similarly shaped cookies. After tasting the treats, mathematicians arrange various quizzes.

11. There is an interesting coincidence. On March 14, the great scientist Albert Einstein was born, who, as you know, created the theory of relativity. Be that as it may, physicists can also join in the celebration of Pi Day.

Every year on March 14, International Pi Day is celebrated. This event, at first glance, is quite insignificant. After all, what is this number "Pi"? Just the ratio of a circle's circumference to its diameter. However, this mysterious number worries the minds of many mathematicians since ancient times. Therefore, several decades ago, scientists agreed to celebrate the annual holiday of the number "Pi". Why March 14th? It's also very simple. In American calculus, this day is written as 3.14 - that is, the first three digits of the number "Pi".

Every year on March 14, International Pi Day is celebrated. This event, at first glance, is quite insignificant. After all, what is this number "Pi"? Just the ratio of a circle's circumference to its diameter. However, this mysterious the number excites the minds of many from ancient times mathematicians. Therefore, several decades ago, scientists agreed to celebrate the annual holiday of the number "Pi". Why March 14th? It's also very simple. In American calculus, this day is written as 3.14 - that is, the first three digits of the number "Pi".

Pi is the most famous constant in the mathematical world.

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 when you divide the circumference of a pumpkin 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 unravel 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.

Men's cologne from the Givenchy company, called "Pi", is designed for attractive and far-sighted people.

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 memory 42,195 decimal places of pi, and is still considered the real champion in this field.

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.

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 one million decimal places in 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 some of the greatest mathematicians of the ancient world, Archimedes from 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 his sword.

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".

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 circle around the known space objects in the Universe, with an error 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.

In mathematics there is infinite set various numbers. Most of them do not attract attention at all. However, some, at first glance, absolutely uninteresting numbers are so well known that they even have their own names. One of these constants is the irrational number Pi, which was studied at school and used to calculate the area or perimeter of a circle along a given radius.

From the history of the constant

Interesting Facts about the number Pi - the history of the study. The existence of a constant counts about 4 millennia. In other words, it is a little younger than the science of mathematics itself.

The first evidence that the number pi was known in ancient Egypt is in the papyrus of Ahmes, one of the oldest problem books found. The document dates from approximately 1650 BC. e. In papyrus, the constant was assumed to be 3.1605. This is a fairly accurate value, given that other peoples used 3 to calculate the circumference of a circle from its diameter.

A little more accurately, the number Pi was calculated by Archimedes, the ancient Greek mathematician. He managed to approximate the value in the form ordinary fractions 22/7 and 223/71. There is a legend that he was so busy calculating the constant that he did not pay attention to how the Romans captured his city. At that moment, when the warrior approached the scientist, Archimedes shouted to him not to touch his drawings. These words of the mathematician were the last.

Al-Khwarizmi, the founder of algebra, who lived in the 8th-9th centuries, worked on the calculations of the constant. With a small error, he received the number Pi, equal to 3.1416.

After 8 centuries, the mathematician Ludolf van Zeulen correctly identified 36 decimal places. For this achievement, the Pi number is sometimes called the Ludolf constant (other well-known names are the Archimedean constant or the circular constant), and the figures obtained by the scientist were engraved on his tombstone.

Around the same time, the constant began to be used not only for a circle, but also for calculating complex curves - arches and hypocycloids.

It was only at the beginning of the 18th century that the constant was called pi. The designation in the form of the letter π was not chosen by chance - it is with it that 2 Greek words begin, meaning circle and perimeter. The name was proposed by the scientist Jones in 1706, and already 30 years later the image of this Greek letter is firmly used among other mathematical notations.

In the 19th century, William Shanks worked on calculating the first 707 characters of a constant. He failed to fully achieve the task - an error crept into the calculations, and the 527 figure turned out to be incorrect. However, even the result obtained was a good achievement for the science of that time.

At the end of the 19th century, the incorrect value of 3.2 was almost accepted at the state level in the state of Indiana. Fortunately, mathematicians managed to oppose the bill and prevent the error.

In the XX-XXI centuries. using computer science the accuracy and speed of calculating the constant has increased thousands of times. By 2002, more than 1 trillion digits of the constant had been determined by computer in Japan. After 9 years, the accuracy of the calculation was already 10 trillion characters after the decimal point.

In art and marketing

Even though pi is a mathematical constant, over the years people have tried to use the irrational and mysterious value in other areas of life, including in works of art.

The very first signs of a constant were found in a monument of architecture in Giza. When determining the size of the Great Pyramid, it turned out that the ratio of the perimeter of its base to the height is π. It is only unknown whether the architect wanted to use his knowledge of this number, or whether such a ratio came out by accident.

Currently, the number Pi is also not deprived of attention in creativity. For example, if you mark each note of the minor scale with a number from 0 to 9, and then play the resulting sequence in the form of pi on a musical instrument, you can enjoy an unusual melody with an interesting sound.

Constant also did not bypass the cinema. The drama film Pi: Faith in Chaos won the Best Director award at the Sundance Film Festival. According to the plot the protagonist is in search of simple and understandable answers to questions about the constant, which as a result almost drove him crazy. References to the number are also found in other movies and TV shows.

The number has found its application even in such an unexpected area as marketing. So, the Givenchy company produced a cologne called "Pi".

Constant and Society

Some features of the number:

The constant is an irrational value. This means that it cannot be represented as a ratio of two numbers. In addition, there is no regularity in his record.
Characters repeating in a row in a constant are not uncommon. So, for every 20-30 characters, there are usually at least 2 consecutive numbers. Sequences of 3 characters are already rarer, they come across with a frequency of about 1 repetition per 150-300 characters. And on the 763rd sign, a chain of 6 consecutive nines begins. This place even has given name is the Feynman point.
If we consider the first million characters, then according to statistics, the rarest numbers in it will be 6 and 1, and the most frequent - 5 and 4.
The number 0 appears in the sequence later than the rest, only on 31 characters.
In trigonometry, a 360 degree angle and a constant are closely related. Oddly enough, but at 358, 359 and 360 positions after the decimal point is the number 360.

In order to exchange information about discoveries, the Pi Club was established. Those wishing to join it have to pass a difficult exam: a future member of the mathematical community must correctly name as many signs of the constant as possible from memory.

Of course, memorizing a long numerical sequence that does not have patterns and repetitions is a rather difficult task. To facilitate the task, various texts and poems are invented in which the number of letters in a word corresponds to a certain number of a constant. This method of memorization is popular with members of the Pi Club. One of the longest stories contained 3834 first digits of the number.

Monument at the Museum of Art in Seattle

However, the recognized champions in memorization are, of course, the inhabitants of China and Japan. So, the Japanese Akira Haraguchi was able to learn over 83 thousand digits after the decimal point. And the Chinese Liu Chao became famous as a man who was able to name 67,890 symbols of the number Pi in a record time of 24 hours. Wherein average speed was 47 characters in 1 minute. Initially, his goal was to name 93 thousand numbers, but he made a mistake, after which he did not continue.

To emphasize the meaning of the constant, a monument in the form of a huge Greek letter π was erected in front of the Museum of Art in Seattle.

In addition, Pi Day has been celebrated every March 14 since 1988. The date coincides with the first signs of the constant - 3.14. Celebrate it after 1:59. On this day, interested people treat themselves to cakes and cookies with the Pi symbol, after which various mathematical contests and quizzes are held. By the way, it was on this day that A. Einstein, the astronomer Schiaparelli and the astronaut Cernan were born.

The number Pi is an amazing constant that has found its application in the most different areas ranging from engineering and construction to the arts. Like any other quantity that is used frequently and which cannot be fully calculated, it will always attract the attention of mathematicians, physicists and other scientists.