PI
The symbol PI means the ratio of the circumference of a circle to its diameter. For the first time in this sense, the symbol p was used by W. Jones in 1707, and L. Euler, having adopted this designation, introduced it into scientific use. Even in ancient times, mathematicians knew that calculating the value of p and the area of a circle were closely related problems. The ancient Chinese and ancient Hebrews considered the number p to be 3. The value for p is 3.1605 found in the ancient Egyptian papyrus of the scribe Ahmes (c. 1650 BC). Around 225 BC e. Archimedes, using inscribed and circumscribed regular 96-gons, approximated the area of a circle using a method that resulted in a PI value lying between 31/7 and 310/71. Another approximate value of p, equivalent to the usual decimal representation of this number 3.1416, has been known since the 2nd century. L. van Zeijlen (1540-1610) calculated the value of PI with 32 decimal places. By the end of the 17th century. New methods of mathematical analysis have made it possible to calculate the p value in many different ways. In 1593 F. Viet (1540-1603) derived the formula
In 1665 J. Wallis (1616-1703) proved that
In 1658, W. Brounker found a representation of the number p in the form of a continued fraction
G. Leibniz published a series in 1673
Series allow you to calculate the p value with any number of decimal places. In recent years, with the advent of electronic computers, p-values have been found with more than 10,000 digits. With ten digits, the PI value is 3.1415926536. As a number, PI has some interesting properties. For example, it cannot be represented as a ratio of two integers or a periodic decimal fraction; the number PI is transcendental, i.e. cannot be represented as a root of an algebraic equation with rational coefficients. The PI number is included in many mathematical, physical and technical formulas, including those not directly related to the area of a circle or the length of a circular arc. For example, the area of an ellipse A is determined by the formula A = pab, where a and b are the lengths of the major and minor semi-axes.
Collier's Encyclopedia. - Open Society. 2000 .
See what "PI NUMBER" is in other dictionaries:
number- Receiving source: GOST 111 90: Sheet glass. Technical specifications original document See also related terms: 109. The number of betatron oscillations ... Dictionary-reference book of terms of normative and technical documentation
Noun, s., used. very often Morphology: (no) what? numbers, what? number, (see) what? number, what? number, about what? about number; pl. What? numbers, (no) what? numbers, why? numbers, (see) what? numbers, what? numbers, about what? about numbers mathematics 1. By number... ... Dmitriev's Explanatory Dictionary
NUMBER, numbers, plural. numbers, numbers, numbers, cf. 1. The concept that serves as an expression of quantity, something with the help of which objects and phenomena are counted (mat.). Integer. A fractional number. Named number. Prime number. (see simple 1 in 1 value).… … Ushakov's Explanatory Dictionary
An abstract designation devoid of special content for any member of a certain series, in which this member is preceded or followed by some other specific member; abstract individual feature that distinguishes one set from... ... Philosophical Encyclopedia
Number- Number is a grammatical category that expresses the quantitative characteristics of objects of thought. Grammatical number is one of the manifestations of the more general linguistic category of quantity (see Language category) along with the lexical manifestation (“lexical... ... Linguistic encyclopedic dictionary
A number approximately equal to 2.718, which is often found in mathematics and science. For example, when a radioactive substance decays after time t, a fraction equal to e kt remains of the initial amount of the substance, where k is a number,... ... Collier's Encyclopedia
A; pl. numbers, sat, slam; Wed 1. A unit of account expressing a particular quantity. Fractional, integer, prime hours. Even, odd hours. Count in round numbers (approximately, counting in whole units or tens). Natural h. (positive integer... encyclopedic Dictionary
Wed. quantity, by count, to the question: how much? and the very sign expressing quantity, number. Without number; there is no number, without counting, many, many. Set up cutlery according to the number of guests. Roman, Arabic or church numbers. Integer, opposite. fraction... ... Dahl's Explanatory Dictionary
NUMBER, a, plural. numbers, sat, slam, cf. 1. The basic concept of mathematics is quantity, with the help of which calculation is made. Integer h. Fractional h. Real h. Complex h. Natural h. (positive integer). Prime number (natural number, not... ... Ozhegov's Explanatory Dictionary
NUMBER “E” (EXP), an irrational number that serves as the basis of natural LOGARITHMES. This real decimal number, an infinite fraction equal to 2.7182818284590..., is the limit of the expression (1/) as n tends to infinity. In fact,… … Scientific and technical encyclopedic dictionary
Quantity, availability, composition, strength, contingent, amount, figure; day.. Wed. . See day, quantity. a small number, no number, grow in number... Dictionary of Russian synonyms and expressions similar in meaning. under. ed. N. Abramova, M.: Russians... ... Synonym dictionary
Books
- Name number. Secrets of numerology. Out-of-body escape for the lazy. Textbook on extrasensory perception (number of volumes: 3), Lawrence Shirley. Name number. Secrets of numerology. Shirley B. Lawrence's book is a comprehensive study of the ancient esoteric system of numerology. To learn how to use number vibrations for...
- Name number. The sacred meaning of numbers. Symbolism of the Tarot (number of volumes: 3), Uspensky Peter. Name number. Secrets of numerology. Shirley B. Lawrence's book is a comprehensive study of the ancient esoteric system of numerology. To learn how to use number vibrations for...
One of the most mysterious numbers known to mankind is, of course, 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 number property, when proven in 1882, 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 meanings from the school curriculum is the 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. The Chinese scientist Liu Hui calculated a value of P that is closer to the modern value; in addition, he invented a quick method for such 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 of modern computers, J. The first measurement was carried out on over 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.
Math enthusiasts around the world eat a piece of pie every year on the fourteenth of March - after all, it is the day of Pi, the most famous irrational number. This date is directly related to the number whose first digits are 3.14. Pi is the ratio of the circumference of a circle to its diameter. Since it is irrational, it is impossible to write it as a fraction. This is an infinitely long number. It was discovered thousands of years ago and has been constantly studied since then, but does Pi still have any secrets? From ancient origins to an uncertain future, here are some of the most interesting facts about Pi.
Memorizing Pi
The record for memorizing decimal numbers belongs to Rajvir Meena from India, who managed to remember 70,000 digits - he set the record on March 21, 2015. Previously, the record holder was Chao Lu from China, who managed to remember 67,890 digits - this record was set in 2005. The unofficial record holder is Akira Haraguchi, who recorded himself on video repeating 100,000 digits in 2005 and recently published a video where he manages to remember 117,000 digits. The record would become official only if this video was recorded in the presence of a representative of the Guinness Book of Records, and without confirmation it remains only an impressive fact, but is not considered an achievement. Math enthusiasts love to memorize the number Pi. Many people use various mnemonic techniques, for example poetry, where the number of letters in each word matches the digits of Pi. Each language has its own versions of similar phrases that help you remember both the first few numbers and the whole hundred.
There is a Pi language
Mathematicians, passionate about literature, invented a dialect in which the number of letters in all words corresponds to the digits of Pi in exact order. Writer Mike Keith even wrote a book, Not a Wake, which is entirely written in Pi. Enthusiasts of such creativity write their works in full accordance with the number of letters and the meaning of numbers. This has no practical application, but is a fairly common and well-known phenomenon in the circles of enthusiastic scientists.
Exponential growth
Pi is an infinite number, so by definition people will never be able to establish the exact digits of this number. However, the number of decimal places has increased greatly since Pi was first used. The Babylonians also used it, but a fraction of three whole and one eighth was enough for them. The Chinese and the creators of the Old Testament were completely limited to three. By 1665, Sir Isaac Newton had calculated the 16 digits of Pi. By 1719, the French mathematician Tom Fante de Lagny had calculated 127 digits. The advent of computers has radically improved human knowledge of Pi. From 1949 to 1967, the number of digits known to man skyrocketed from 2,037 to 500,000. Not long ago, Peter Trueb, a scientist from Switzerland, was able to calculate 2.24 trillion digits of Pi! It took 105 days. Of course, this is not the limit. It is likely that with the development of technology it will be possible to establish an even more accurate figure - since Pi is infinite, there is simply no limit to accuracy, and only the technical features of computer technology can limit it.
Calculating Pi by hand
If you want to find the number yourself, you can use the old-fashioned technique - you will need a ruler, a jar and some string, or you can use a protractor and a pencil. The downside to using a can is that it needs to be round and accuracy will be determined by how well a person can wrap the rope around it. You can draw a circle with a protractor, but this also requires skill and precision, as an uneven circle can seriously distort your measurements. A more accurate method involves using geometry. Divide the circle into many segments, like a pizza into slices, and then calculate the length of a straight line that would turn each segment into an isosceles triangle. The sum of the sides will give the approximate number Pi. The more segments you use, the more accurate the number will be. Of course, in your calculations you will not be able to come close to the results of a computer, however, these simple experiments allow you to understand in more detail what the number Pi is and how it is used in mathematics. 
Discovery of Pi
The ancient Babylonians knew about the existence of the number Pi already four thousand years ago. Babylonian tablets calculate Pi as 3.125, and an Egyptian mathematical papyrus shows the number 3.1605. In the Bible, Pi is given in the obsolete length of cubits, and the Greek mathematician Archimedes used the Pythagorean theorem, a geometric relationship between the length of the sides of a triangle and the area of the figures inside and outside the circles, to describe Pi. Thus, we can say with confidence that Pi is one of the most ancient mathematical concepts, although the exact name of this number appeared relatively recently.
New look at Pi
Even before the number Pi began to be correlated with circles, mathematicians already had many ways to even name this number. For example, in ancient mathematics textbooks one can find a phrase in Latin that can be roughly translated as “the quantity that shows the length when the diameter is multiplied by it.” The irrational number became famous when the Swiss scientist Leonhard Euler used it in his work on trigonometry in 1737. However, the Greek symbol for Pi was still not used - this only happened in a book by a lesser-known mathematician, William Jones. He used it already in 1706, but it went unnoticed for a long time. Over time, scientists adopted this name, and now it is the most famous version of the name, although it was previously also called the Ludolf number.
Is Pi a normal number?
Pi is definitely a strange number, but how much does it follow normal mathematical laws? Scientists have already resolved many questions related to this irrational number, but some mysteries remain. For example, it is not known how often all the numbers are used - the numbers 0 to 9 should be used in equal proportion. However, statistics can be traced from the first trillions of digits, but due to the fact that the number is infinite, it is impossible to prove anything for sure. There are other problems that still elude scientists. It is possible that further development of science will help shed light on them, but at the moment it remains beyond the scope of human intelligence.
Pi sounds divine
Scientists cannot answer some questions about the number Pi, however, every year they understand its essence better and better. Already in the eighteenth century, the irrationality of this number was proven. In addition, the number has been proven to be transcendental. This means that there is no specific formula that allows you to calculate Pi using rational numbers. 
Dissatisfaction with the number Pi
Many mathematicians are simply in love with Pi, but there are also those who believe that these numbers are not particularly significant. In addition, they claim that Tau, which is twice the size of Pi, is more convenient to use as an irrational number. Tau shows the relationship between circumference and radius, which some believe represents a more logical method of calculation. However, it is impossible to unambiguously determine anything in this matter, and one and the other number will always have supporters, both methods have the right to life, so this is just an interesting fact, and not a reason to think that you should not use the number Pi.
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 were discovered. But the most important thing is that there are no repetitions in the decimal part of pi, as in an ordinary 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 all the prime numbers. 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 the recipe for making bechamel sauce, and all the holy books of all religions. This is a 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 the world literature that has already been written (in particular, those books that burned, etc.), but also all the books that WILL yet 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 messages that the Old Testament supposedly contains 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 they are currently calculated to 12411 trillionth sign!!!
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. Of course, the exact value of the number was not immediately calculated. 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 at the beginning of the 18th century (1706) and comes from the initial letters of 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 among different peoples, the number Pi had different meanings. For example, in Ancient Egypt it was equal to 3.1604, among the Hindus it acquired a value of 3.162, and 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 exchange knowledge and new information about Pi, a Pi Club was organized. 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 for remembering 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.
If you compare circles of different sizes, you will notice the following: the sizes of different circles are proportional. This means that when the diameter of a circle increases by a certain number of times, the length of this circle also increases by the same number of times. Mathematically this can be written like this:
| C 1 | C 2 | ||
| = | |||
| d 1 | d 2 | (1) |
where C1 and C2 are the lengths of two different circles, and d1 and d2 are their diameters.
This relationship works in the presence of a coefficient of proportionality - the constant π already familiar to us. From relation (1) we can conclude: the length of a circle C is equal to the product of the diameter of this circle and a proportionality coefficient π independent of the circle:
C = π d.
This formula can also be written in another form, expressing the diameter d through the radius R of a given circle:
С = 2π R.
This formula is precisely the guide to the world of circles for seventh graders.
Since ancient times, people have tried to establish the value of this constant. For example, the inhabitants of Mesopotamia calculated the area of a circle using the formula:
Where does π = 3 come from?
In ancient Egypt, the value for π was more precise. In 2000-1700 BC, a scribe called Ahmes compiled a papyrus in which we find recipes for solving various practical problems. So, for example, to find the area of a circle, he uses the formula:
| 8 | 2 | |||||
| S | = | ( | d | ) | ||
| 9 |
From what reasons did he arrive at this formula? – Unknown. Probably based on his observations, however, as other ancient philosophers did.
In the footsteps of Archimedes
Which of the two numbers is greater than 22/7 or 3.14?
- They are equal.
- Why?
- Each of them is equal to π.
A. A. Vlasov. From the Examination Card.
Some people believe that the fraction 22/7 and the number π are identically equal. But this is a misconception. In addition to the above incorrect answer in the exam (see epigraph), you can also add one very entertaining puzzle to this group. The task reads: “arrange one match so that the equality becomes true.”
The solution would be this: you need to form a “roof” for the two vertical matches on the left, using one of the vertical matches in the denominator on the right. You will get a visual image of the letter π.
Many people know that the approximation π = 22/7 was determined by the ancient Greek mathematician Archimedes. In honor of this, this approximation is often called the “Archimedean” number. Archimedes managed not only to establish an approximate value for π, but also to find the accuracy of this approximation, namely, to find a narrow numerical interval to which the value π belongs. In one of his works, Archimedes proves a chain of inequalities, which in a modern way would look like this:
| 10 | 6336 | 14688 | 1 | |||||||||
| 3 | < | < | π | < | < | 3 | ||||||
| 71 | 1 | 1 | 7 | |||||||||
| 2017 | 4673 | |||||||||||
| 4 | 2 | |||||||||||
can be written more simply: 3,140 909< π < 3,1 428 265...
As we can see from the inequalities, Archimedes found a fairly accurate value with an accuracy of up to 0.002. The most surprising thing is that he found the first two decimal places: 3.14... This is the value we most often use in simple calculations.
Practical use
Two people are traveling on a train:
- Look, the rails are straight, the wheels are round.
Where is the knock coming from?
- Where from? The wheels are round, but the area
circle pi er square, that’s the square that knocks!
As a rule, they become acquainted with this amazing number in the 6th-7th grade, but study it more thoroughly by the end of the 8th grade. In this part of the article we will present the basic and most important formulas that will be useful to you in solving geometric problems, but to begin with we will agree to take π as 3.14 for ease of calculation.
Perhaps the most famous formula among schoolchildren that uses π is the formula for the length and area of a circle. The first, the formula for the area of a circle, is written as follows:
| π D 2 | |
| S=π R 2 = | |
| 4 |
where S is the area of the circle, R is its radius, D is the diameter of the circle.
The circumference of a circle, or, as it is sometimes called, the perimeter of a circle, is calculated by the formula:
C = 2 π R = π d,
where C is the circumference, R is the radius, d is the diameter of the circle.
It is clear that the diameter d is equal to two radii R.
From the formula for circumference, you can easily find the radius of the circle:
where D is the diameter, C is the circumference, R is the radius of the circle.
These are basic formulas that every student should know. Also, sometimes it is necessary to calculate the area not of the entire circle, but only of its part - the sector. Therefore, we present it to you - a formula for calculating the area of a sector of a circle. It looks like this:
| α | |||
| S | = | π R 2 | |
| 360 ˚ |
where S is the area of the sector, R is the radius of the circle, α is the central angle in degrees.
So mysterious 3.14
Indeed, it is mysterious. Because in honor of these magical numbers they organize holidays, make films, hold public events, write poems and much more.
For example, in 1998, a film by American director Darren Aronofsky called “Pi” was released. The film received many awards.
Every year on March 14 at 1:59:26 a.m., people interested in mathematics celebrate "Pi Day." For the holiday, people prepare a round cake, sit at a round table and discuss the number Pi, solve problems and puzzles related to Pi.
Poets also paid attention to this amazing number; an unknown person wrote:
You just have to try and remember everything as it is - three, fourteen, fifteen, ninety-two and six.
Let's have some fun!
We offer you interesting puzzles with the number Pi. Unravel the words that are encrypted below.
1. π R
2. π L
3. π k
Answers: 1. Feast; 2. File; 3. Squeak.
