History of the vindication of zero. Mathematics project on the topic: "Division is the number zero" When you show up 0

Who guessed zero? For those who want to reject Swedish evidence, I will say that Indian mathematicians invented zero. So it’s the official history of mathematics. But for those who are very keen and ready to read this article to the end, I will say that it was not only Indian mathematicians who were at fault. It's just a little bit more zero.
Before speech, how to speak correctly "zero" or else "zero" There is no important meaning. In mathematics, it is customary to write the number zero - “zero” (“equal to zero”, “less than zero”), but in everyday life it is often called “zero”.
Let's go back to the history of the number zero and the number zero. The number zero, which we are now using, came to us from the Arabic numerals, which were lost to Arabic mathematicians from India. It was then that India itself introduced the ten position system. How could they have done it earlier? rahuvati without zero? I could and I couldn’t at the same time. What is similar to zero even appears on the clay cuneiform tablets of ancient Babylon.

For example, the Babylonians, not knowing about zero, simply divided the numbers 202 into 22. They wanted to use a sixdecimal number system, and not a ten like we have, they intuitively understood, which means zero. In an empty box, either three “tacks” or two blades were written down, which were marked as empty. It was still close to 300 years before our era.

The ancient Greeks had a lot of knowledge about zeros. This is because the Greeks operated with numbers mainly for applied purposes of geometry. And the last cut is equal to zero and has no practical value. In astronomical numbers, the letter "omicron" (όμικρον) was stagnant. The main letter of the word "ouden" which means nothing and is written as O (circle) and means .... No, not zero, but 70! The Greeks developed an alphabetic system for recording numbers.

The Romans did not know about zero. How to write the number 388 in Roman numerals in CCCLXXXVIII. Good idea about discharging.

And in ancient Greece and Egypt, stones were made for rahanku. If the stone rises from the place on which it was lying behind the frame, the hole is lost. Chi is not zero? No, not yet zero. Everything that was before the Indians was of little more than an applied nature and in no way can be taken as a true history of the output of zero. There is no need for an empty container.

The system of tens of discharges originated in China. To write down the number 934, 4 sticks were placed on one hundred, 3 sticks on tens, and 9 sticks on hundreds. Instead of zero, they deprived the empty place. And the axis of recording Chinese digits did not change and there was no symbol for zero.

The so popular infection of the Indians, Maya, also had its own zero in the current twenty-decimal number system, a thousand years earlier than the Indians. Ale zero in the Maya means not zero in the common word, but “cob”. The cycle of days in the Mayan calendar began with day zero and was called Ahau.

The Inca neighbors used a sheet of paper, where the numbers 1 to 9 were marked with different knots, and zero with an empty space.

Why did Indian mathematicians come to power? They wrote down the zero precisely, indicating the daily number, then with a circle. Alas, they meant zero not as an understanding of the subsistence of a number, but as a number.
Around 500 years of our era, the positional system of recording numbers was broken down, and the record, which involves the replacement of zero, dates back to 876 years.

Indian mathematicians Brahmagupta, Mahavira and Bhaskara wrote that if you take out one number, you get zero. This is the meaning of the number zero that we know. Now zero is not a number. Zero is vikoristovuyutsya in the decomposition and it is written like a small circle. With just 10 digits you can write down the largest number. There was a revolution in mathematics.

Indians called zero "sunka" empty. The Arabs transferred the tse yak "sifr", what does the word sound like? "digits". Before the speech, Indian mathematicians

The concept of zero appeared and came to a sense quite recently - only in the 5th century AD. Until now, mathematicians have been trying to figure out more than the simplest arithmetic concepts.

The concept of zero appeared and came to a sense quite recently - only in the 5th century AD. Until now, mathematicians have been trying to figure out more than the simplest arithmetic concepts. Today, zero as a symbol (or number) is a concept that means the presence of any quantity that allows us to solve problems and solve problems.

It is important to note that the first system of rakhunku appeared among the Sumerians. Later, they significantly improved upon Babylon. In the Sumerian racket system, the meaning of a symbol was completely dependent on the position of many other symbols. Robert Kaplan, author of the book “The Natural History of Zero,” suggests that the distant ancestor of the current zero was a pair of heap wedges, which were used to show that the stopper at the table was empty. The days of Babylon never developed the idea of ​​zero in the form of a number.

Six hundred years later, mathematicians taught the Mayan people the concept of “empty”, like zero in their folding calendar tables. Zero serves as a border between the old and new cycle. However, the equals and fathers have zero, as before, without vikorism.

It has long been said that Indian mathematicians traced the concept of zero to the Babylonians. Others, however, respect that the Indian zero, as a number, developed independently. The first understanding of zero appeared in India around the beginning of the 5th century AD. Mathematical equations were laid out in the form of poetry and songs, and were indicated by symbols. Words such as “empty”, “sky” and “spread” initially symbolized zero. And 628 years ago, the Indian astronomer and mathematician Brahmagupt put the abstract concept of zero into a symbol - a dot. In addition, we have developed mathematical operations with vicoristics of numbers, written rules for reaching zero by the way of folding and solving, and also by observing the results of vicorising zero in equal numbers. The very first thing is zero knowledge, not just as an idea, but as a number.

Over the course of several centuries, the concept of zero as a number has gained popularity both in China and locally. And zero became an invisible part of the Arabic system of disbursements, which was based on the Indian system. The Persian mathematician Mohammed, in addition to zero, developed the methods of rapid multiplication and the division of numbers, which are known as algorithms. A little while later, I made my way to Europe.

The Italian mathematician Fibonacci pioneered the calculations, which inevitably became the most widely used tools for the development of arithmetic operations and gained great popularity among traders. By the beginning of the 16th century, zero was widely used throughout Europe. This idea spurred and accelerated the development of the rectilinear coordinate system of Rene Descartes, inspired by Isaac Newton and Gottfried Wilhelm. In addition, the very same science as physics has begun to develop and become increasingly rich, and as a result, there are current technological developments, including the ever-popular computers.

It may be true that zero is the only part of any system of numbers, and mathematics is impossible without it, but this is corrected by the recent finding. In fact, this ubiquitous symbol of “superness” appeared in Europe only during the period of the Protogenny, and more precisely, in the 12th century.

The first zero in history: Sumeri and Maya

This is consistent with most historical thoughts, first appearing in the native valley of Mezhirichya, in ancient Mesopotamia. The Sumerians indicated the presence of digital digits in their numerical columns even another thousand years before the star. That is, the first zero symbol appeared in the written records of the third century BC. e. from ancient Babylon. The Babylonians adopted the sixtieth number system, in which zero served to distinguish numerical values ​​in the same manner as today we use tens, hundreds, thousands, and so on. In this case, having lost the sense of zero in Babylonia.

This is the very symbol that is used in the same way, having appeared in the Indian Mayan tribe in about 350 people. Many ancient civilizations did not give zero any more mathematical significance.

Mathematical value: India and the Near Meeting

Early civilizations valued zero as a significant number of digits, rather than as a number in its own right for its mathematical powers and characteristics. The mathematical value of zero was first recognized in India, in the 7th century. The mathematician and astronomer Brahmagupta recognized the “zero” value of zero and called it sunya, which in translation means “empty.” Brahmagupta was the first to master mathematical operations with zero.

From India the zero migrated to the Near Descent and the territory of the great Babylon. The Persian mathematician Abu Ablullah, or Muhammad ibn Musa al-Khorezmi, in 773 years, conquered zero in the levels of algebra. In the 9th century, the Arabic numeral “0” appeared, with practically the same oval shape as we have today. It’s cool that the Indian “sunina” was translated into Arabic and turned into the word “sifr”, which is similar to the word “digit”.

Suchasne zastosuvannya: Europe

Europe is only a hundred miles away. The first mysteries about him date back to the 12th century. The works of Leonardo of Pisa, best known under the nickname Fibonacci, helped to popularize the zero and introduce it widely. The concept of “substance” played an important role in the theories of rich scholars such as Descartes, Newton and Leibniz. Since then, without zero, there is no need for a numerical system.

Beforehand, we need to guess that the digits of the number are not the same. We call numbers special signs that represent numbers.


The answer to who came up with such icons, and who became the first to use them, is not so simple. Obviously, people began to appreciate it from the very beginning, and then they learned that in the world everything can be suppressed, everything can be assigned a numerical value. Having learned, people began to think about this in order to indicate numbers using special signs.

Top digital symbols

From the very beginning there were notches, which were made with a stick on soft material, or were scratched. One notch is the number 1, two are 2 or so. Moreover, in the documents that were preserved, the number of notches corresponded to the number that was expressed - for example, a thousand. Almost a century has passed since people first came up with the idea of ​​assigning ranks to numbers and denoting great quantities with adjacent signs. Tse obviously forgot the entry,

It is important that the first numerical symbols appeared in ancient Egypt and in ancient Babylon. The Egyptians developed a hieroglyphic sheet, in which numbers were indicated by risks, and ranks - by special symbols. To begin with, there were stylized images of the sacred Egyptian creature - the intestine.

The ancient Babylonians created a great shave for the designated numbers. They have found the positional record which has the meaning of the sign in sequence. In Babylonia, they used a hexadecimal number system, which corresponds to the hour (our year is divided into 60 khvilin, khvilin - into 60 seconds).

The ancient Romans guessed their numbers. Roman numerals are still in use, but the sphere of their stagnation is strictly limited. Roman numerals indicate, for example, the numbers of sections in a book. Having looked at these signs, you can immediately understand that they trace their history back to the simplest notches - marks.


Roman numeric notation is not positional: understand that a number is indicated by digits, you can perform simple arithmetic operations - intricacies and add numbers using a simple algorithm. It is very difficult to write down large quantities in Roman numerals, but it is practically impossible to use the entries for calculation.

Did the stars come up with the current numbers?

The credit for finding the current numbers (and their importance in the current numbers) goes to the Indians. In the fifth century of our era, the smells generated the most important insight: they introduced the concept of zero into mathematical practice and guessed the sign for it - empty, circled in a circle. Since the discovery of zero was important, it was important to mention the fact that the word itself is translated from Arabic "Sifr"(what does our "number" ) means zero itself. The Indians wrote down other numbers from 1 to 9 using simple symbols similar to those we use today.

The Indians began to represent numbers in a positional way, when the number of tens, hundreds, thousands and other digits was represented by one digit, which was worth a position. This tradition of stench was adopted from the Babylonians. It has become possible not only to write down any numbers from zero to infinity, but also to carry out mathematical operations with them.

How did Indian numbers reach Europe and why do we call them Arabic? The Arabs were in close contact with the Indians and carried on lively trade. In addition, science, culture and business were actively developing in the Arab countries at that time, and for this it was necessary to study mathematics. The Arabs adopted Indian numerals and began to profit from them.

In front of her, people who first established the tenth positional recording of numbers using the Indian method and popularized this idea in the Arab world. This is the famous teaching of Muhammad ibn Musa al-Khorezmi, who wrote his famous treatise on arithmetic. The book contains the basics of Indian architecture and digital recording.

This happened in the 9th century of our era. The new system quickly expanded to the Close Convergence, and in the 10-13th centuries it spread to Europe. In European countries, Arabic numerals were initially used when marking coins, then when numbering the pages of books, documents, etc.


The Arabic digital recording system allowed humanity to achieve great strides in science, economy, and education. This system can be learned by any preschooler, it has become popular, and we rarely realize that in order to write down great numbers people had to make small sticks or draw a gut on papyrus!

Do you know that from the beginning the calculation system is not small in its stock of numbers zero? Our ancestors faded logically: now they go out and find out the number, which means “nothing”, empty place? How did people get by without zero?
Moreover, the first calculation systems were non-positional, then. The skin symbol signifies the song's strength, regardless of which one, this symbol was used to record the number. The butt of such a non-positional system, which we use until now, may be Roman numbering. Roman numerals are used, for example, when indicating centuries (V century BC, XXI century), in the names of individuals of royal blood (Mikola I, Louis XIV) or when numbering sections and divisions in books. This system has a zero per day calculation, it is simply not required. So, to write down the number 30, three X symbols are used to represent ten - XXX. The number 105 looks like CV, where C means a hundred, and V means five.

Everything is simple. However, for the skin category (ones, tens, hundreds, thousands, etc.) you need to change your sign. The larger the number, the more discharges in your warehouse, the more complete and confused your record becomes. Thus, on the pedestal of the Copper Peak in St. Petersburg, the designations of the rivers of the monument are similar to the Roman calculation system - MDCCLXXXII, which corresponds to the number 1782. As you see, it’s difficult to understand such a record, even though there are more than four ranks present among those present. Well, it’s practically impossible to work on expansion in such a charging system.

How the ancient Romans managed to add, add and add other mathematical operations with numbers written with sticks, crosses, checkmarks, etc. symbols? In fact, special shell boards – abaci – were built for the openings. An example of such a primitive calculating device can be the shells that accountants and cashiers used to use until recently. The abacus consisted of several sections, the skin of which was representative of its category. In this way, to indicate the number 206, the first section, which represents singles, had 6 items added, the third (hundred) had 2, and the other, which could have dozens, did not put anything. This empty place with time turned to zero. As it seems, zero appeared practically from nothing.

Of course, it didn’t turn out that well. The first tried to replace the empty space at the discharge with the number 0 of the mathematics of ancient Babylon. Their calculation system was positional, then. all ranks were indicated by the same signs, but for the recording of the skin of the attack, they were moved to the left of the previous one. As soon as there was a discharge, a clearing was created. The opposite zero appeared in India. Indian mathematicians adopted the principle of positionalism of the Babylonians and the tenth system adopted by China. Ten signs began to be used to record numbers. And the first zeros were a little smaller behind the digits and looked like small stakes. Then this symbol was transformed into the current zero.

The introduction of the zero and tens positional system has become a useful concept in mathematics. The Arabs, who established this system of enumeration among the Indians, further developed and perfected it. For a long time, a symbol that means zero, called the word “digit” (from the Arabic “sifr” - zero). Later, in the 16th century, all symbols of the Arabic number system began to be called numbers. And zero has taken away its personal name, which is similar to the Greek word “nullus” - yellow.

At the beginning of the 18th century, the Arabic system of rakhunku began to stagnate everywhere, zokrema. that of Europe. And with success, vikoryst and dosi.