Arabic numerals and numbers. Arabic numerals or Indian ones? Why are numbers called Arabic?

Throughout most of ancient history, man had little need for numbers. Before the invention of agriculture, people lived by hunting and gathering, taking only as much as they needed, and a little more for reserve or for exchange. Therefore, they had nothing to count.

In ancient times, primitive numerical records were made in the form of notches on a stick, knots on a rope, laid out in a row of pebbles. But the names of numbers were not directly used to read such numerical records.

Savages account

Even when people invented counting, they first counted only what was of value to them. And now in Papua New Guinea the Yupno tribe counts wicker baskets, grass skirts, pigs and money, but not people, not nuts and not bags of potatoes.

Many tribes count by fingers and toes (base 20, i.e., twenties). The number 10 is designated as 2 hands, 15 - 2 hands and a foot, 20 - one person.

Other tribes start counting with the little finger, go up to the thumb, then the palm, the whole arm, the torso and only then the second hand. The Fayvol tribe has 27 body parts and uses their names as numbers. For example, 14 is the nose, for numbers greater than 27 1 person is added, 40 is 1 person and the right eye.

The history of the appearance of numbers. Counting on fingers was very widespread, and it is quite possible that the names of some numbers originate precisely from this method of counting.

People learned to count numbers back in the Stone Age - Paleolithic, tens of thousands of years ago. At first, people only compared different quantities of identical objects by eye. They could determine which of the two heaps had more fruit, which herd had more animals, etc.

Then numerals appeared in the human language, and people were able to name the number of objects, animals, days. For many peoples, the name of the number depended on the items being counted. We still use different numerals with the meaning “many”: “crowd”, “herd”, “flock”, “heap”, etc.

4). The connection between fingers and numbers has existed since ancient times.

Fingers helped people find a very convenient way to count even before they came up with names for numbers.

When you touch your fingers when counting something, you will never make a mistake.

Counting on fingers was very widespread, and it is quite possible that the names of some numbers originate precisely from this method of counting. Even today we use the English word “digits” which means finger.

The name of the numbers from one to ten is easy to remember, because we have ten fingers on our hands, and this is a kind of memory system.

2. Number systems.

1). Base 10.

Mathematicians say that our number system is based on 10, that is, in groups of ten.

There is no mathematical explanation for why we count this way. Once people started counting, they apparently used their fingers to do so. Since all humans have ten fingers, it made sense to count in tens. This is where our decimal number system came from.

This happened only thanks to human biology. We have 10 fingers.

If there are aliens who have eight fingers, they probably count with eights.

2). Ways to write numbers.

To record numbers before the advent of writing, notches on sticks, notches on bones, and knots on ropes were used. When writing appeared, numbers appeared to record numbers. .

In mathematics, such an alphabet is numbers, and words are numbers. There are many similarities: number systems are unique languages in mathematics. In such alphabets, the letters are numbers.

To perform operations on numbers, the numbers themselves must be designated somehow. After all, it’s not so easy, even with numbers (the symbols used to write numbers), to write down some number. To do this, you need a number system (a way of writing numbers using digits). You can, of course, come up with a new designation for each new number. While people knew few numbers, they did so. .

3). Unit number system.

Uncivilized tribes, whose counting needs, as a rule, did not go beyond the top ten, began to use the unit number system.

Such a system of numbers is called unit, because any number in it is formed by repeating one sign, symbolizing one.

The unit number system of primitive people is not forgotten even today. How to find out what course a military school cadet is studying? Count how many stripes are sewn on the sleeve of his uniform. The number of aircraft shot down by an ace in air battles is indicated by the number of stars painted on the fuselage of his aircraft.

This is the simplest, but absolutely inconvenient number system. Based on a single digit - one (stick). Allows you to write only natural numbers. To represent a number in this number system, you need to write down as many sticks as the number itself. Just imagine the number 1000 written with a bunch of pebbles, and 1,000,000? Uncomfortable?

Then people began to figure out how to write large numbers differently. To begin with, they decided to replace every 10 sticks with a squiggle, and the counting became easier!

4. Historically established number systems in different countries. The concept of number is one of the basic concepts of modern mathematics. It is one of the oldest concepts. All cultural peoples who possessed writing had the concept of number and certain number systems. Moving around the countries, you can get acquainted with the different number systems of the peoples of the world.

1). Notation of numbers in Egypt.

The very first number system was apparently invented in the Ancient East (in Egypt or Mesopotamia). From these inscriptions we know that the ancient Egyptians used only the decimal number system. A unit was designated by one vertical line, and to indicate numbers less than 10, it was necessary to put the corresponding number of vertical strokes.

10 40 To designate the number 10, the basis of the system, the Egyptians, instead of ten vertical lines, introduced a new collective symbol, reminiscent of a horseshoe in its outline. If you need to depict several dozen, then the hieroglyph was repeated the required number of times. This also applies to other hieroglyphs. As a result, the ancient Egyptians could represent numbers up to a million.

100 1 000 10 000 100 000 1 000 000 10 000 000

The introduction of digital notations by the Egyptians marked one of the important stages in the development of number systems.

2). Designation of numbers in Babylon. In ancient Babylon, about 40 centuries before our time, positional numbering was created, that is, a way of writing numbers in which the same number can represent different numbers, depending on the place occupied by this number.

One vertical wedge-shaped line meant one; repeated the required number of times, this sign served to record numbers less than ten; To represent the number 10, the Babylonians, like the Egyptians, introduced a new collective symbol - a wider wedge-shaped sign with the tip pointing to the left, resembling an angle bracket in shape.

1 ppr - 10 - 0

Repeated an appropriate number of times, this sign served to represent the numbers 20, 30, 40 and 50).

3). Notation of numbers in ancient America.

The Mayans lived in Central America during the first millennium and, during their heyday, had one of the most advanced cultures of this period. .

Their achievements in the fields of astronomy and mathematics were truly amazing. As Europe trudged through the Dark Ages, Mayan priests and astronomers determined from the sun that the length of the year was 365.242 days (modern measurement: 365.242198), and the length of the lunar cycle was 29.5302 days (modern measurement: 29.53059) . Such amazingly accurate results were hardly possible without a powerful number recording system. Mayan numerals are positional notation based on the base 20 number system. Mayan numbers were composed of three elements: zero (shell sign), one (dot) and five (horizontal line). For example, 19 was written as four dots in a horizontal row above three horizontal lines.

The Mayan Indians also had a hieroglyphic recording of numbers.

1 2 3 4 5 6 7 8 9 10

4). Notation of numbers in Greece and Russia.

In Ancient Greece, they did it very simply: the Greeks did not invent special symbols for numbers, but used letters. One was designated by the letter A, two by B, three by D, and four by D.

The Greek alphabet is very similar to the Russian one, since the Slavic alphabet was created on the basis of Greek by the monks Cyril and Methodius. In order not to confuse numbers with letters, a dash was placed above them. Together with the alphabet, this system of writing numbers came to Ancient Rus'.

The Slavic alphabetical system for writing numbers is based on the Cyrillic alphabet. It was used in Russia until the 1700s, when Peter I replaced it with Arabic numerals.

5). Roman numerals.

Ancient Greek numerals remained only in history, but we continue to use ancient Roman numerals. Why do we still use this inconvenient number system? Probably because in this way you can distinguish some numbers from others.

The “finger” origin of the decimal system is confirmed by the shape of the Latin numerals: the Latin numeral V is a palm with a protruding thumb, and the Roman numeral X is two crossed hands

Roman number notation:

1- I 5 – V 10 – X 50 – L 100 – C 500 – D 1000 - M

To consolidate in memory the letter designations of numbers in descending order, there is a mnemonic rule: We Give Juicy Lemons, Vsem Ix is Enough. Accordingly M, D, C, L, X, V, I

6). Designation of numbers in China.

The Chinese number system is one of the oldest.

It arose as a result of operating with sticks laid out on a table or board for counting.

There was another number system in China, which is one of the oldest and most progressive, since it contained the same principles as the modern Arabic one that we use. This numbering arose about 4,000 thousand years ago.

7). Notation of numbers in India.

Very few written monuments of ancient Indian civilization have survived, but, apparently, Indian number systems went through the same stages in their development as in all other civilizations.

Inscriptions dating back to the first centuries BC and the first centuries AD appear to contain notations for numbers that were the direct predecessors of those now called the Indo-Arabic system. Initially, this system had neither a positional principle nor a zero symbol.

Indian mathematicians already 300 BC. e. invented separate symbols to represent numbers from 1 to 9.

Around 600 AD e. in India they used the zero symbol, and therefore the positional number system.

8). Designation of numbers in Arabia. At first, the Arabs wrote numbers in words, but then, as the Greeks had done earlier, they began to denote numbers with the letters of their alphabet.

The year 711 can be considered the year of the discovery of these figures in the territories of the Middle East; they, of course, came to Europe much later. The fact is that the wonderful city of Bakhda - or as we used to call it - Baghdad in those days was quite an attractive place for scientists. In 711 there was a treatise on the stars “Siddanta” and at the same time about numbers. In 772, the Indian treatise Siddanta was brought to Baghdad and translated into Arabic, after which two systems for writing numbers began to be used:

1). In astronomy, the alphabetic system was still used.

2). In trade payments, merchants began to use a system borrowed from India.

5. Distribution of Arabic numbers.

A manual compiled at the beginning of the 9th century by Muhammad Al Khwarizmi played a decisive role in the spread of Indian numbering in Arab countries. The brilliant work of Indian mathematicians was adopted by Arab mathematicians, and Al-Khwarizmi in the 9th century wrote the book “The Indian Art of Counting” or “Kitab al-jabr wa-l-muqabala”, in which he describes the decimal positional number system. The words "arithmetic" and "algorithm" come from his name, and the word "algebra" comes from the title of his book.

In the 12th century. Juan of Seville translated this book into Latin, and the Indian system of counting spread widely throughout Europe. And since Al-Khorezmi’s work was written in Arabic, the Indian numbering in Europe received the wrong name - “Arabic”. This historical misnomer continues to this day. The word “digit” (in Arabic “syfr”), literally meaning “empty space” (translation of the Sanskrit word “sunya”, which has the same meaning), was also borrowed from the Arabic language.

Moroccan historian Abkelkari Boujibar believes that the Arabic numerals in their original version were given meaning in strict accordance with the number of angles that form the figures. Thus, one creates only one angle, three - three, five - five, etc. zero does not form any angle, therefore it has no content.

Arabic numerals. 1234567890 - these numbers are called Arabic, although the Arabs only transferred to Europe the method of writing numbers developed by the Indians.

The Arabs chose the most successful ones from various types of numbers. By camel and ship they carried Indian numerals and figures west to Baghdad, the center of the newly created Muslim empire. From them the numbers continued their journey across the Earth. The form we now use was established in the 16th century. In Europe, Australia and both Americas, people use Arabic numerals to write numbers, although the Arabs themselves do not use them and have never used them.

The real homeland of this numbering is India. Europeans, having borrowed numbering from the Arabs, called it “Arabic”.

Arabic numerals in European form 0 1 2 3 4 5 6 7 8 9 Actually Arabic numerals used in Arab countries ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩..

I conducted several experiments trying to perform mathematical operations using different number systems. Of the possible options, I looked for the most convenient way and came to the following conclusions.

1. The hypothesis that Arabic numerals were invented by the Arabs was not confirmed.

2. In fact, the numerals and numbers we call Arabic were invented in India.

3. The invention of decimal positional numbering by Indians in the 6th century is rightfully considered one of the greatest achievements of mankind.

4. The name “Arabic numerals” was formed historically, due to the fact that it was the Arabs who spread the decimal positional number system.

5. The numbers used in Arab countries are very different from the “Arab” ones.

Municipal educational institution Pokrovskaya secondary school Municipal Educational Institution "Tsilninsky District" Ulyanovsk Region

Design and research work

"The Secret of the Origin of Arabic Numerals"

Bazunov Evgeniy,

5th grade student

Municipal educational institution Pokrovskaya secondary school.

Scientific adviser -

Uraksina Evgenia Viktorovna,

mathematic teacher

Municipal educational institution Pokrovskaya secondary school.

With. Pokrovskoe

Table of contents

INTRODUCTION……………………………………..……………………………………………………….….… 3

CHAPTER 1.What is a number?……….……………………….………………………………... 4

CHAPTER 2. Numbers of ancient peoples

Numbers in Ancient Egypt………………….……………………………………………………………….. 5

Figures in Babylon………………………………….………………………………………………………..… 6

Numbers in Ancient Greece…………………………..…..……………………………..….. 7

Roman numbering………………………………………..………………………………..… 8

Slavic Cyrillic numbering……………….………………………..….. 9

CHAPTER 3. The secret of the origin of Arabic numerals …………………………..… 11

CHAPTER 4.Organization and conduct of the study………………………. 14

Conclusion…………………………………………………………...…………………………….…… 16

Literature………………………………………………………….……………………………. 17

Application

Appendix 1 ………………………………………………………………………………….. 18

Appendix 2………………………………………………………………………………….. 20

Appendix 3………………………………………………………………………………….. 22

INTRODUCTION

“Everything is a number,” said the Pythagoreans. I absolutely agree with them. Both before and now a person is surrounded by numbers: the cost of purchase, phone number, date of birth, grades at school, etc. Numbers are made up of digits. How did numbers arise, what were the different writing options for numbers, what is common in their writing, what are the rules for composing numbers from numbers?

These questions have always interested me. And one day I thought about the followingproblem: why do we, people living in Russia, use Arabic numerals? And how “Arabic” are Arabic numerals? Since I love both mathematics and history, I decided to devote my project to answering these questions.

So , the goal of my project is find out the secret of the origin of Arabic numerals and the reason for their longevity.

To achieve my goal I need to decide the followingtasks :

With the help of literary sources and the Internet, get acquainted with the numbers of different nations.

Find information about the origin of Arabic numerals.

Compare different number systems to understand why modern people use Arabic numerals.

Research the level of knowledge of the people around me about the numbers that they all use.

Create a presentation that reflects the results of my design and research work.

Thus , object my research begannumbers of different peoples, ancient numbers, modern numbers.

When I begin my work, I put forwardhypothesis : There is a certain mystery in the origin of Arabic numerals, but we still use them, since they are the most convenient.

Basic research methods : literature analysis, comparison, student survey, Internet resources, analysis and synthesis of data obtained during the study.

CHAPTER 1

What is a number?

Number - basic concept , used for characteristics, comparisons, and their parts. Written signs to denote numbers are , and mathematical . Having appeared back in from needs , the concept of number has expanded significantly with the development of science.

The concept of number arose in ancient times, approximately 4-5 thousand years ago. It developed from the practical needs of people in the process of human development. The scope of human activity expanded and, accordingly, the need for quantitative description and research increased. At first, the concept of number was determined by the needs of counting and measurement that arose in human practical activity, becoming more and more complex. Later, number becomes the basic concept of mathematics, and the needs of this science determine the further development of this concept.

People knew how to count objects back in ancient times, and then the concept of a natural number arose. At the first stages of development, the concept of an abstract number was absent. In those days, a person could estimate the quantities of homogeneous objects called in one word, for example, “three people”, “three axes”. In this case, different words were used: “one”, “two”, “three” for the concepts “one person”, “two people”, “three people” and “one ax”, “two axes”, “three axes”. This is shown by the analysis of the languages of primitive peoples. Such named number series were very short and ended with the non-individualized concept “many”. Different words for a large number of different kinds of objects still exist, such as “crowd”, “herd”, “heap”. Primitive counting of objects consisted of “comparing objects of a given specific collection with objects of a certain specific collection, playing, as it were, the role of a standard,” which for most peoples were fingers (“counting on fingers”). This is confirmed by linguistic analysis of the names of the first numbers. At this stage, the concept of number becomes independent of the quality of the objects being counted.

Several decades ago, archaeological scientists discovered a camp

ancient people. In it they found a wolf bone, on which 30 thousand years ago some hunter made 55 notches. It is clear that while making these notches, he was counting on his fingers.

Chapter 2

Numbers of ancient peoples.

Numbers in Ancient Egypt

The first written figures for which we have reliable evidence appeared in Egypt and Mesopotamia about 5,000 years ago.

In Ancient Egypt, cursive hieroglyphic writing was formed, and Mesopotamian scribes used cuneiform. Therefore, the Egyptian first numerals conveyed in their form the nature of all surrounding objects: animals, plants, household items, etc. The Rhinda papyrus (1650 BC) and the Golenishchev papyrus (1850 BC) - numerical ancient Egyptian documents - testify to the high cultural development of the people. Mesopotamian cuneiform is depicted on clay tablets, on which the numbers are represented by small wedges turned in different directions according to their meaning. Both Egyptian and Mesopotamian number systems had numbers from 1 to 10, special marks to represent tens, hundreds and thousands, and zero, which was represented by a highlighted blank space. The numbers of ancient Egypt are constructed competently and logically. Rationalism and clarity distinguish these number systems from similar attempts by other peoples. Numbers with a value less than ten were designated׀ . For example, the number 6 looked like׀׀׀׀׀׀ . The number 10 was denoted by an inverted horseshoe in the hieroglyphic system and by a special symbol in the hieratic system. There are as many “horseshoes” in a number as there are tens. The hieratic writing system assumed a separate symbol for each number, ten higher than the previous one. Starting from 100, it was a stylized stick, above which a tiny mark was placed with each new hundred.

Everything is simpler in hieroglyphs. The number 100 looked almost like the Arabic numeral 9, but the Egyptians called it the lotus. Then everything is the same: “lotus”, 300 – 3, etc.

Have you noticed that ancient Egypt had a decimal system from the very beginning? However, Mesopotamia still surpassed Egypt when Babylon gained independence on its territory and rose to prominence.A separate culture grew there, nurtured by the achievements of neighboring conquered states.

Numbers inBabylon

The numbers of ancient Babylon differed little from those of Mesopotamia: the same wedge-shaped signs served to designate units -˅ , and tens -˃ . The combination of these signs was used to represent the numbers 11-59. The number 60 in the letter looked like a mirror image of the letter "G". 70 – G˃ , 80 - G˃˃ and so on, the principle is clear, cuneiform is not distinguished by genius.

The main value is that the same sign - note - depending on where it is located in the notation of the number, has a different meaning. We are talking about the placement of signs in the number system. The same wedge-shaped signs indicated in different categories have different significance. Therefore, the Babylonian number system with zero is usually called positional. Mathematicians can argue with this, because not a single source has been found in which the zero would be located at the end of the numerical notation, which indicates relative positionality.

The Babylonian system became a kind of springboard from which humanity made a leap to a new stage of its development. The idea eventually fell into the hands of the Indians. They made their own adjustments, improving the number system. The idea was adopted by Italian traders who brought it to Europe along with their goods. The positional number system has spread all over the world, enriching with its appearance not only mathematical sciences, but also modern counting.

Numbers in AncientGreece

The Greeks used several ways to write numbers.There were two main number systems in use in Ancient Greece -

Attic (or Herodian) and Ionic (also Alexandrian or

alphabetical). When using Ionic numbering, numbers were expressed by letters of the alphabet. To distinguish a number from a word, a special icon was placed above the letters of the number- title This method of writing numbers was used by the inhabitants of Miletus and Alexandria. The Athenians used the first letters of numerals to denote numbers:

G (Γέύτέ) - five,

Δ(Δέκά) - ten,

Χ(Χιλιάό) - thousand,

Μ(Mυριάό) - ten thousand,

I, II, III, IIII - respectively 1, 2, 3, 4
ΔΔΔIIII - 10+10+10+4=34

With the help of these numbers, a resident of Ancient Greece could write down any, not very large, number. The great Greek mathematician Diophantus of Alexandria wrote fractions in approximately the same way that is pleasant now: the numerator is above the denominator, but without a line. This was one of the ways to write fractions in Ancient Greece.

The second Ionic number system adopted in Ancient Greece is

alphabetical - became widespread in the early

The Alexandrian era, although it could have arisen several centuries earlier, apparently already among the Pythagoreans. To distinguish numbers from words, the Greeks placed a horizontal line above the corresponding letter. Similarities between the Greek letter O and the modern one

the designation zero may be something more than a coincidence, but we do not have precise data to say this with certainty. Writing in alphabetic characters could be done in any order, since the number was obtained as the sum of the values of individual letters.

Up to Greek mathematics did not stand out in any way. As usual, counting and measurement were mastered. Greek numeration (recording numbers), like later Roman numeration, was additive, that is, the numerical values of digits were added. The counting board was arranged accordingly ( ) with pebbles. By the way, the termcalculation (calculation) comes fromcalculus - pebble. A special holey pebble indicated zero.

IN the “Greek miracle” begins: two scientific schools appear at once -( , , ) And . We know about the achievements of early Greek mathematicians mainly from mentions of later authors, mainly commentators, And .

Roman numbering

The Roman numbering system using letters was common in Europe for two thousand years. Only in the late Middle Ages was it replaced by a more convenient decimal system of numbers, borrowed from the Arabs. But, to this day, Roman numerals are used to indicate dates on monuments, time on clocks, and (in the Anglo-American typographic tradition) pages of book prefaces. In addition, in Russian it is customary to use Roman numerals to denote ordinal numbers.

To designate numbers, 7 letters of the Latin alphabet were used: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Intermediate numbers were formed by adding several letters to the right or left. First thousands and hundreds were written, then tens and units. Thus, the number 24 was depicted as XXIV. A horizontal line above the symbol meant multiplication by a thousand.

Natural numbers are written by repeating these numbers. Moreover, if a larger number is in front of a smaller one, then they are added (the principle of addition), but if a smaller number is in front of a larger one, then the smaller one is subtracted from the larger one (the principle of subtraction). The last rule applies only to avoid repeating the same number four times. For example, I, X, C are placed respectively before X, C, M to indicate 9, 90, 900 or before V, L, D to indicate 4, 40, 400. For example, VI = 5+1 = 6, IV = 5 - 1 = 4 (instead of IIII). XIX = 10 + 10 - 1 = 19 (instead of XVIIII), XL = 50 - 10 =40 (instead of XXXX), XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33, etc.

Performing arithmetic operations on multi-digit numbers in this notation is very inconvenient. The Roman numeral system is not currently used, with the exception, in some cases, of designating centuries (XV century, etc.), AD. e. (MCMLXXVII, etc.) and months when indicating dates, ordinal numbers, and sometimes derivatives of small orders.

Slavic Cyrillic numbering

This numbering was created together with the Slavic alphabetic system to translate the sacred biblical books for the Slavs by the Greek monks brothers Cyril and Methodius in the 9th century. This form of writing numbers became widespread due to the fact that it was completely similar to the Greek notation of numbers. Until the 17th century, this form of recording numbers was official in the territory of modern Russia, the Republic of Belarus, Ukraine, Bulgaria, Hungary, Serbia and Croatia. Until now, Orthodox church books use this numbering.

Numbers were written from digits in the same way from left to right, from large to small. Numbers from 11 to 19 were written in two digits, with the unit coming before the ten.

We read literally “fourteen” - “four and ten”. As we hear, we write: not 10 + 4, but 4 + 10, - four and ten (or, for example, 17 - seven-ten). Numbers from 21 and above were written in reverse, with the full tens sign written first. The number notation used by the Slavs is additive, that is, it only uses addition.

In order not to confuse letters and numbers, titles were used - horizontal lines above the numbers, which we see in our drawing. To indicate numbers greater than 900, special icons were used that were drawn around the letter. This is how the following large numbers were formed:

Slavic numbering existed until the end of the 17th century, until a positional decimal number system - Arabic numbers - came to Russia from Europe with the reforms of Peter I.

An interesting fact is that almost the same system was used by the Greeks. This is precisely what explains the fact that for the letterbthere was no digital value. Although, there is nothing particularly surprising here: the Cyrillic numbering is completely copied from the Greek. The Goths also had similar numbers.

Chapter 3

The secret of the origin of Arabic numbers

The history of our familiar “Arabic” numbers is very confusing. It is impossible to say exactly and reliably how they happened. One thing is certain: it is thanks to the ancient astronomers, namely their precise calculations, that we have our numbers. Between the 2nd and 6th centuries AD. Indian astronomers became acquainted with Greek astronomy. They adopted the sexagesimal system and roundGreek zero. The Indians combined the principles of Greek numbering with the decimal multiplicative system taken from China. They also began to denote numbers with one sign, as was customary in the ancient Indian Brahmi numbering. The brilliant Seville translated this book into Latin, and the Indian system of counting spread widely throughout Europe.

Indian arose in not later . At the same time, the concept was discovered and formalized ( Shunya ), which allowed us to go to .

Arabic and Indo-Arabic numerals are modified styles of Indian numerals, adapted to .

The Indian recording system was widely popularized by the scientist , author of the famous work “ ", from whose name the term " " Al-Khwarizmi wrote a book “On Indian Accounting”, which contributed to the popularization records of numbers throughout the Caliphate, up to . contains the first mention and image of Arabic numerals (except ) V . They appeared through in Spain around 900.

Arabic numerals became known V . Thanks to close connections ( ) And ( ), ( With By ) had the opportunity to access scientific information that no one in the then . In particular, he was one of the first among Europeans to become acquainted with Arabic numerals and understood the convenience of their use compared to and began to promote their introduction into European science. IN Al-Khorezmi’s book “On Indian Accounting” was translated into Latin and played a very important role in the development of European arithmetic and the introduction of Indo-Arabic numerals. The name “Arabic numerals” was formed historically, due to the fact that it was the Arabs who spread Reckoning. The numbers used in Arab countries are very different in design from those used in European countries.

In the old Babylonian texts dating back to 1700 BC, there is no special sign for zero; it was simply left with an empty space, more or less highlighted.

Arabic numerals (sans serif font)

Writing numbers

The writing of Arabic numerals consisted of straight line segments, where the number of angles corresponded to the size of the sign. Probably, one of the Arab mathematicians once proposed the idea of linking the numerical value of a number with the number of angles in its writing.

Let's look at the Arabic numerals and see that

0 is a number without a single angle in the outline.

1 - contains one acute angle.

2 - contains two acute angles.

3 - contains three acute angles (the correct, Arabic, number shape is obtained when writing the number 3 when filling out the postal code on the envelope)

4 - contains 4 right angles (this explains the presence of a “tail” at the bottom of the number, which does not in any way affect its recognition and identification)

5 - contains 5 right angles (the purpose of the lower tail is the same as the number 4 - completion of the last corner)

6 - contains 6 right angles.

7 - contains 7 right and acute angles (the correct, Arabic, spelling of the number 7 differs from that shown in the figure by the presence of a hyphen crossing the vertical line at a right angle in the middle (remember how we write the number 7), which gives 4 right angles and 3 angles gives still the upper broken line)

8 - contains 8 right angles.

9 - contains 9 right angles (this is what explains the intricate lower tail of the nine, which had to complete 3 corners so that their total number becomes equal to 9.

In the modern world we use Arabic numerals. Because they are more convenient to write. Their system is called decimal, in order to write a number we need only 10 digits: 0 1 2 3 4 5 6 7 8 9. And not, like the Slavs, more than 50. And with the help of these numbers we can write any number without limitation. Also, thanks to the zeros invented by Muslims, writing has become much easier. Therefore, nowadays Arabic numerals are considered the most convenient and simplest.

Also on the Internet I found an interesting number translator program Titlo_0.12.2. You can find out more about it in the Appendix.

CHAPTER 4

Organization and conduct of research

The study was conducted among 5th grade students and an online survey (Appendix 1). A total of 30 people were interviewed.

Students and Internet users were asked 4 questions:

1.What numbers do we use in the modern world?

2. Where did the numbers come to us from?

3. Where did the concept of zero originate?

Research results:

Question 1: What numbers do we use in the modern world?

Looking at the diagram, we see that the majority of respondents were not mistaken and chose the correct answer. In the modern world we use Arabic numerals.

Question 2: Where did the numbers come from?

The respondents failed to answer the second question. Most answered that the numbers came to us from Arabia. And only 10 people chose the correct answer: the numbers came to us from India.

Question 3: Where did the concept of zero originate?

Most of the respondents answered the third question incorrectly, since zero was invented in India. During the research process, I noticed that the respondents were not sure of the correct answer.

Question 4:Using the table (Appendix 2) for writing numbers of different nations, write the numbers: 4, 10, 325, 543, in Egyptian (hieroglyphs), in Babylonian, in Greek, in Roman, in Slavic.

Coped with the writing (out of 30 participants).

Slavs

skies

From this table we see that the most difficult writing of numbers is Slavic. Also, the more characters in a number increased, the more difficult its writing became.

Conclusion

The goal of my project was to find out the secret of the origin of Arabic numerals and the reason for their longevity. To achieve it, I had to solve the assigned tasks. That's what came out of it.

Task No. 1 – with the help of literary sources and the Internet, get acquainted with the numbers of different nations. In the course of solving this problem, I became acquainted with the numbers of Ancient Egypt, Babylon, ancient Greece and Rome, and did not ignore Slavic Cyrillic numbering and, of course, Arabic numbers. I think that within the framework of this project, the problem has been solved 100%. And it’s great that work in this direction can be continued, because there are still many different numberings, both studied and unstudied. In the future, I would like to study in more detail the figures of the great Mayan civilization.

Task No. 2 - find information about the origin of Arabic numerals. I also completely coped with this task thanks to the Internet and the book by N.Ya. Vilenkin "Behind the pages of a mathematics textbook." Indeed, the history of the origin of Arabic numerals turned out to be very confusing. I realized that it is not entirely correct to call our numbers Arabic. They concentrated the experience of many civilizations: Egyptian, Babylonian, Greek, and, of course, Indian. Yes, the Arabs added a lot of their own to the Indian number system, and it was the Arabs who spread these numbers throughout Europe, but it would be unfair to consider them only an Arab achievement.

Task No. 3 is to compare different number systems in order to understand why modern people use Arabic numerals. I believe that I managed to figure out this problem too. Unfortunately, I had to admit that our Slavic numbers are extremely inconvenient to use. I can imagine how confused modern schoolchildren would be with letters and numbers if we still used Slavic numbering. The convenience of Arabic numbering is obvious:

The Arabic number system is positional, i.e. the meaning of a digit depends on its place in the notation of the number; it contains the concept of “zero” and that is why, with the help of just ten digits, we have the opportunity to write absolutely any number!

Task No. 4 is to explore the level of knowledge of the people around me about the numbers that they all use. This problem was solved using a survey of school students and an Internet survey. I found that most of the respondents knew that we use the Arabic number system, but very few people had any idea where our numbers came from and where the concept of zero originated. It was with great difficulty that respondents wrote down modern numbers in other number systems. Moreover, the biggest difficulty was writing the number in Slavic numerals. While working in this direction, I made my own little discovery - I discovered a program - a number translator (Titio _0.12.2).

Task No. 5 - creating a presentation that would reflect the results of my design and research work - was also solved.

I believe that I have achieved my goal and completed all the tasks. My hypothesis was completely confirmed: the history of Arabic numerals is full of mysteries, and the longevity of the Arabic number system is associated with its convenience. I really enjoyed working with the project. In the future, I want to continue working in this direction, since now I am interested in the issue of the magic of numbers.

The magic of numbers is the energy of God,

Mathematics of letters,

You have to work for a very long time,

To know your spirit.

Glagolitic alphabet and back. Also "Titlo" can translatefigures of nations: Chinese, Armenian, Georgian, Greek (Ionian and Attic), Roman, Jewish numbers, Mayan numbers and others.

The ranges of numbers in "Titlo" are small, but quite sufficient for most of the needs of numismatists, philatelists and second-hand booksellers when determining dates and denominations on coins, stamps and books. However, Titlo can also help amateur historians.

For some numbers, different letters were used at different times, or the appearance of these letters changed. Therefore, additional buttons are given for such numbers - the one with a checkmark under it is used. All switches innumber translatorcan be done with the number already dialed - the changes will immediately be displayed in the final window.

Story emergence numbers very deep and long-standing. Life itself has led people to the point where it has become simply necessary to use symbols to write numbers.

Imagine, a long time ago, when people didn’t have numbers and couldn’t count like we do now, they still had a huge number of reasons to count. True, in those days they did not need to use huge numbers. And the simplest version of the account was suggested by nature. People used their fingers, and in larger numbers, their feet, to count, for example, the number of heads of cattle in a herd. If your own fingers weren’t enough, you called a friend so you could count on his hands and feet. It was quite inconvenient, but what if no one was around when you urgently needed to count a large amount of something?

History of numbers

Then someone came up with the idea of making clay circles for counting. For example, a shepherd led a large flock to pasture in the morning. I counted all the animals using circles - how many circles, so many animals. In the evening he brought them home and again made sure that each animal had one circle. Well, there were many similar options, that is, they used improvised means.

The first evidence of the use of counting by ancient people is a wolf bone, which was notched 30 thousand years ago. Moreover, they are not stuffed somehow, but grouped in groups of five.

Antiquity.

In Antiquity, different peoples had their own methods of counting. For example, the Mayans used only three symbols: a point, a line and an ellipse and used them to write down any numbers.

In Ancient Egypt around 5000-4000 BC. used the following notation of numbers: one was denoted by a stick, a hundred by a palm leaf, and one hundred thousand by a frog (there were a lot of frogs in the Nile Delta, so people had this association: one hundred thousand is a lot, like there are a lot of frogs in the Nile).

But our Slavic ancestors used the most complex notation of numbers. They wrote them down in letters, above which they put a special “title” icon to distinguish where they wrote the letters and where the numbers were, and they had as many as 27 icons.

And, for example, the Papuan tribes had only two numbers, one and two, and called them “urapun” and “okosa”, respectively. And further numbers were called simply using these two. For example, three of them are “Okoza-Urapun”, and four are “Okoza-Okoza”. Apparently, they don’t have much to count, so they don’t have large numbers. And they call everything more than six or seven “a lot.” And how many “many” there are is no longer known!

Cuneiform.

But humanity developed, the economy expanded, and calculations became more complicated. There was a need to write down numbers. After all, it is impossible to remember from memory how many heads of cattle there are in the herd, how many bags of wheat you have, and how much you spent, how much you planted and what harvest you harvested. And at about V century BC the first numbers appeared.

They say that the first numbers were invented by the Sumerians, a people who lived in the territory of the Southern Interfluve of the Tigris and Euphrates, modern Iraq, approximately IV-III millennium BC The Sumerians, by the way, are a very interesting people. A huge number of inventions known today were first used by them. For example, baked brick, wheel.

The Sumerians also invented the so-called cuneiform writing or cuneiform. Various symbols in the form of wedges were drawn on clay tablets. The Sumerian civilization was very advanced for those times. Traders and artisans lived in their cities. Clay chips of various shapes were first used for counting. Over time, marks began to be made on them, indicating the quantity and type of what was being counted. For example, two goats. But the two bags wrote completely differently. That is, they described the number of specific objects and did not highlight a separate figure.

After the Sumerians, the Babylonians settled in these lands. They adopted the Sumerian number system. The Egyptians also used a similar counting system.

But still, this way of writing numbers is not ideal, and with the development of mankind, the writing of numbers also developed.

Roman numerals appeared 500 BC. The Roman number system was very common in Europe and was considered ideal at that time until Arabic numerals were invented.

I - 1

V- 5

X -10

L- 50

C -100

D- 500

M -1000

With small numbers it is quite convenient, but for writing large numbers it is very difficult. Another drawback: it is impossible to do calculations in writing. They can only be done in the mind, which, naturally, can give rise to a large number of errors.

Nowadays Roman numerals are also used, for example, in recording the century, the serial number of the monarch, etc.

In V century, a writing system appeared in India, which we know as Arabic numerals and are actively using now. It was a set of 9 numbers from 1 to 9. Each number was written so that it corresponded to the number of angles. For example, in number 1 there is one angle, in number 2 there are two angles, in number 3 there are three. And so on until 9. Zero did not exist yet, it appeared later. Instead, they simply left an empty space.

Then something interesting happened: the Arabs adopted the Indian number system and began to use it with all their might. In those days, the Muslim world was very developed, it had very close ties with Asian and European culture and took from them everything that was most perfect and advanced at that time.

Mathematician Muhammad Al-Khwarizmi IX century compiled a guide to Indian numbering. It's in XII century came to Europe and this number system became very widespread. It’s interesting, but precisely because these numbers came to us from the Arabs, we call them Arab, not Indian.

By the way, the word “digit” itself is of Arabic origin. The Arabs translated the Indian “sunya” and it turned out to be “digits”.

The Arabic number system is called positional. This means that the meaning of a number depends on its position in the record. That is, in the number 18 the number 8 means 8 ones, and in the number 87 the same eight means 8 tens. Positional systems are the most advanced. But they originated from non-positional systems (which, in principle, still exist) as a result of the development of humanity, its knowledge and needs.

The interesting thing is that modern Arabic numerals are very different from those we use:

Like this history of numbers. Nowadays different numbers are also used. Some countries, such as Arab countries and China, use their own special numbers. But, nevertheless, the most widespread are Arabic numerals, which are used and understood all over the world.