Indo-Arabic and Arabic figures are considered modified by the inscriptions of the oldest Indian figures, which were subsequently added to the Arab letter.
Arabic scientist Abu Jafar Muhammad Ibn Musa Al-Khorezmi was impressed with opening prospects when using Indian numbers, and he tried to popularize them with all their might. By the way, the word "algebra" originated from the name of the famous Labor Abu Jafar "Kitab Al-Jebr Va-L-Mukabala". Subsequently, the scientist wrote a work that called "On Indian Account". This book contributed to a greater popularity of the positional decimal system of a numerical record in the entire Muslim world, including Spain.
The very first mention and drawing of Arabic numbers (without zero) in Europe can be found in the Wigilan Code. At first, these figures brought Maur to Spain at about 900
Read more: who are such GOG and Magog
The photo of the helmet is well visible to the artfully applied golden drawing of the royal crown with the Orthodox eight-pointed cross. On the steel arrow of the protective nose, the drawing of Archangel Mikhail made enamel. And the most interesting thing, around the circumference next to the edge of the helmet, the belt written by Arabic Vseu. The inscription is clearly seen, it is written there. " Va Bashir Almuminine"What can be translated as" and are coming orthodox. "The helmet was made by the Russian master Nikita Davydov, who combined on his product, like Arabica and Slavic sacred symbols. Please note that the Russian inscriptions are not available on it at all. Nikita wrote Only in Arabic, and this may mean that until the 17th century in Russia, Islam was a state religion and only subsequently gradually replaced in Christianity.
What people came up with Arabic numbers
MOU Pokrovskaya SOSH MO "Tsilninsky district" of the Ulyanovsk region
Design - research work
"The secret of the origin of Arabic numbers"
Bazunov Eugene,
grade 5 student
MOU Pokrovskaya Sosh.
Scientific adviser -
Urstina Evgeny Viktorovna,
mathematic teacher
MOU Pokrovskaya Sosh.
from. Pokrovskoe
Table of contents
Introduction ...................................................................................................... ... 3
CHAPTER 1.What is the number? ........................................................................................ ... 4
Chapter 2. Figures of the Ancient Peoples
Figures in ancient Egypt ............................................................................ .. 5
Figures in Babylon ................................................................................................... .. ... 6
Figures in ancient Greece ................................................................................... .. ... .. 7
Roman numbering………………………………………..………………………………..… 8
Slavic Cyrillic numbering ................... ........................... .. ... .. 9
Chapter 3. The secret of the origin of Arabic numbers .............................. .. ... 11
Chapter 4.Organization and conducting research ............................ fourteen
Conclusion ...................................................... ... .......................................... 16
Literature .................................................................................................................. 17.
application
Appendix 1 ........................................................................................................... .. 18
Appendix 2 ........................................................................................................... .. 20
Appendix 3 ........................................................................................................... .. 22
Introduction
"All there is a number" - said Pythagoreans. I absolutely agree with them. And before and now, a person surrounds numbers: the cost of buying, phone number, date of birth, school mark, etc. Numbers are made up of numbers. How the figures arose, what were the options for writing numbers from different peoples, which is common in writing them, what are the rules for compiling numbers from numbers?
These questions have always been interested in me. And once I thought about the nextproblem: why do we, people living in Russia, use Arabic figures? And how much are Arabic figures? Since I love both mathematics, and history, I decided to devote my project answers to these questions.
so , the purpose of my project is find out the secret of the origin of Arabic numbers and the reason for their long-lived.
To achieve the goal, I need to solve the following tasks :
With the help of literary sources and the Internet, to get acquainted with the numbers of different nations.
Find information on the origin of Arabic numbers.
Compare various number systems to figure out why modern people use the Arabic figures.
Explore the level of knowledge of the people around me about the numbers that they all use.
Create a presentation in which to reflect the results of my design - research work.
In this way , object my research has becomefigures of different peoples, ancient digits, modern numbers.
Getting to your work, I put forward hypothesis : In the origin of Arabic numbers there is a certain mystery, and we still use them so far, as they are the most comfortable.
Basic research methods : Analysis of literature, comparison, survey of students, resources from the Internet, analysis and generalization of the data obtained during the study.
CHAPTER 1
What is the number?
Number - Basic concept , used for characteristics, comparisons, and their parts. Written signs to designate numbers serve , as well as mathematical . Arriving more B. from needs The concept of a number with the development of science has significantly expanded.
The concept of the number appeared in ancient times, about 4 5 thousand years ago. From the practical need of people and developed in the process of human development. The field of human activity has been expanding and, accordingly, increased the need for a quantitative description and study. At first, the concept of the number was determined by the needs of the invoice and measurements that arose in the practical activity of a person, and more complicated. Later, the number becomes the basic concept of mathematics, and the needs of this science determine the further development of this concept.
It was still in ancient times to consider objects, then the concept of natural number arose. At the first levels of development, the concept of an absent number was absent. In those days, a person could evaluate the number of homogeneous objects, called in one word, for example, "three people", "three axes". At the same time, various words "one" "two", "three" for the concepts of "one person", "two people", "three people" and "one ax", "two axes", "three axes". This shows an analysis of the languages \u200b\u200bof primitive peoples. Such named numeric rows were very short and ended with an unindlyued concept of "a lot." Different words for a large number of items of different kinds exist now, such as "crowd", "flock", "bunch". The primitive account of the subjects was "in comparison of items of this particular combination with subjects of some definite totality, which plays as it were for the role of standard", which most peoples had fingers ("the score on the fingers"). This is confirmed by a linguistic analysis of the names of the first numbers. At this stage, the concept of the number becomes independent of the quality of those considered objects.
Several tens of years ago, archaeologists discovered the country
ancient people. In it, they found a wolf bone, on which 30 thousand years ago, some kind of hunter fell 55 scubons. It can be seen that, making these scubons, he believed on his fingers.
Chapter 2.
Figures of ancient peoples.
Figures in ancient Egypt
The first written figures we have reliable evidence appeared in Egypt and Mesopotamia about 5,000 years ago.
In ancient Egypt, a speed-up hieroglyphic letter was formed, Mesopotamian scribes were used clig. Therefore, the Egyptian first figures were transferred by their form of all surrounding items: animals, plants, household items, etc. Rinda Papirus (1650 BC) and Papyrus Gorenishchev (1850 BC) - Numerical ancient Egyptian documents - indicate the high cultural development of the people. Mesopotamian clinows are captured on clay signs, on which the numbers are represented by small wedges, turned into different directions according to their meaning. And in Egyptian, and in Mesopotamian surgery systems there are numbers from 1 to 10, special labels for the designation of dozens, hundreds and thousands, and zero, which were denoted by a high-width place. The numbers of ancient Egypt are built competently and logical. Rationalism and clarity are distinguished by these number systems from similar attempts by other peoples. The numbers less than ten were denoted׀ . For example, the figure 6 looked like׀׀׀׀׀׀ . The number 10 was designated in the hieroglyphic system and a special symbol in the hieratic. How many dozens are among, so much and "horseshoes". The heeratical system of writing assumed for each number, a dozen above the previous one, a separate character. Starting from 100, it was a stylized key, over which the tiny note was put on each new hundred.
In hieroglyphs everything is easier. The number 100 looked almost like the Arabic number 9, but the Egyptians called it by the lotus. Further, all similar: "Lotus", 300 - 3, etc.
Have you noticed that in ancient Egypt from the very beginning a decimal system was formed? However, Mesopotamia nevertheless surpassed Egypt when independence has gained independence and climbed Babylon.There grown a separate culture, focused by the achievements of neighboring conquered states.
Figures B.Babylon
The numbers of the ancient Babylon had little difference from Mesopotamian: the same wedges served to designate units -˅ , and dozens -˃ . The combination of these marks was used to designate numbers 11-59. The number 60 in the letter looked like a mirror reflection of the letter "g". 70 - G.˃ 80 - g˃˃ And so on, the principle is clear, the clinies are not distinguished by genius.
The main value is that the same sign - pay attention - depending on where it is located in the number of numbers, it has a different meaning. We are talking about the local placement of signs in the number system. The same wedge-shakes specified in different discharges have different significance. Therefore, the Babylonian numbering system with zero is customary called the positional. Mathematics can argue with this, because no source is found, in which the zero would have been located at the end of the numerical record, which speaks of relative positionality.
The Babylonian system has become a kind of springboard, from which humanity made a jump on a new stage of its development. The idea over time fell into the hands of the Hindus. They made their own adjustments by improving the number system. They adopted the idea of \u200b\u200bItalian merchants who brought her to Europe along with the goods. The positional surgery flew around the world, enriching its appearance not only mathematical sciences, but also a modern account.
Figures in the ancientGreece
Greeks used several ways to write numbers. In ancient Greece, there were two main number systems -
attic (or Gerodian) and Ionical (she is Alexandria or
alphabetic). When using the ionic numbering, the numbers were expressed by the letters of the alphabet. To distinguish the number from the word, a special icon set over the letters-
titlo.
This method of recording numbers was applied by the inhabitants of Milet and Alexandria. Athenians, for the designation of numbers, used the first letters of words-numerals:
G (γέύτέ) - five
Δ (Δέκά) - ten,
Χ (χιΛάόάό) - a thousand
Μ (mυριάό) - ten thousand,
I, II, III, IIII - compliant 1, 2, 3, 4
ΔΔIIIIi - 10 + 10 + 10 + 4 \u003d 34
With the help of these figures, a resident of ancient Greece could record any, not very large, number. The great Greek mathematician Diofant Alexandria recorded the fraction as well as nice now: Numerator over the denominator, but without a feature. It was one of the ways to record fractions in ancient Greece.
The second adopted in ancient Greece ionic survey system -
alphabetic - gained widespread in the beginning
Alexandrian era, although it could arise in several centuries earlier, apparently, already in the Pythagoreans. To distinguish the numbers from words, the Greeks above the corresponding letter set a horizontal line. The similarity of the Greek letter O with modern
the designation of the zero can be something large than a random coincidence, but we have no accurate data that make it possible to assert this with all certainty. The recording of alphabetical symbols could be made in any order, since the number was obtained as the sum of the values \u200b\u200bof individual letters.
Up to greek mathematics did not stand out anything. There were, as usual, the score and measurement were mastered. Greek numbering (recording of numbers), as later Roman, was additive, that is, the numeric values \u200b\u200bof the numbers were evolved. Accordingly, a countable board was arranged ( ) With pebbles. By the way, the termcalculation (calculation) comes fromcalculus. - pebbles. Special leaky pebbles indicated zero.
IN the "Greek Miracle" begins: two scientific schools appear at once - (,,) and . On the achievements of early Greek mathematicians, we know mainly on mentioning the later authors, mostly commentators , and.
Roman numbering
The Roman numbering system with the help of letters was distributed in Europe for two thousand years. Only in the late Middle Ages it changed more convenient for calculations a decimal system of numbers borrowed from the Arabs. But, so far, the Roman numbers are denoted by the dates on the monuments, time on the clock and (in the Anglo-American typographical tradition) of the book of book prefaces. In addition, in Russian, Roman numbers are customary to designate ordinal numerals.
To designate numbers, 7 letters of the Latin alphabet were used: i \u003d 1, v \u003d 5, x \u003d 10, l \u003d 50, c \u003d 100, d \u003d 500, m \u003d 1000. The intermediate numbers were formed by adding several letters to the right or left. First, thousands and hundreds were written, then dozens and units. Thus, the number 24 has been depicted as XXIV. The horizontal line above the symbol meant multiplication per thousand.
Natural numbers are recorded using the repetition of these numbers. At the same time, if a large figure stands in front of the smaller, then they fold (the principle of addition), if the smaller - before greater, then the smaller is deducted from the greater (the principle of subtraction). The latter rule applies only to avoid the four-time repetition of the same number. For example, I, X, C are applied according to x, s, m to designate 9, 90, 900 or before V, L, D to denote 4, 40, 400. For example, Vi \u003d 5 + 1 \u003d 6, IV \u003d 5 - 1 \u003d 4 (instead of IIII). XIX \u003d 10 + 10 - 1 \u003d 19 (instead of XVIIII), XL \u003d 50 - 10 \u003d 40 (instead of xxxx), xxxiii \u003d 10 + 10 + 10 + 1 + 1 + 1 \u003d 33, etc.
Performing arithmetic actions on multi-valued numbers in this record is very uncomfortable. The system of Roman figures is not currently applied, except, in some cases, the designations of the centuries (XV century, etc.), the years. e. (Mcmlxxvii, etc.) and months when specifying dates, sequence numbers, as well as sometimes derived small orders.
Slavic Cyrillic numbering
This numbering was created together with the Slavic alphabetic system for the transfer of sacred biblical books for Slavs by Greek monks by Brothers Kirill and Methodius in the 9th century. This form of the number of numbers was widely distributed due to the fact that there was a complete resemblance to the Greek records of numbers. Until the XVII century, this form of recording numbers was official in modern Russia, the Republic of Belarus, Ukraine, Bulgaria, Hungary, Serbia and Croatia. Until now, Orthodox church books use this numbering.
The numbers were recorded from numbers as to the left, to the right, from large to the smaller. The numbers from 11 to 19 were recorded by two digits, and the unit went before the top ten.
We read literally "Fourteen" - "Four and Ten". As hearing, and write: not 10 + 4, and 4 + 10, - four and ten (or, for example, 17 - sem-on-ten). The numbers from 21 and higher were recorded on the contrary, first wrote a sign of complete dozens. The record of the number used by the Slavs additive, that is, it uses only addition.
In order not to confuse letters and numbers, the title was used - horizontal dashes over the numbers that we see in our illustration. To refer to the numbers of large than 900, special icons were used, which were drawn around the letter. So the following large numbers were formed:
Slavic numbering existed until the end of the XVII century, while Peter I's reforms in Russia from Europe did not come a positional decimal number system - Arab numbers.An interesting fact that almost the same system was also used in Greeks. This is what explains what for the letterb.there was no digital value. Although nothing particularly amazing here is not: Cyrillic numbering is completely copied with Greek. Close numbers were and ready.
Chapter 3.
The secret of the origin of the Arab numbers
The story of our usual "Arab" numbers is very confused. It is impossible to say exactly and reliably as they occurred. One thing is exactly known that it is thanks to the ancient astronomers, namely, with their exact calculations we have our numbers. Between II and VI centuries AD. Indian astronomers became acquainted with Greek astronomy. They adopted the sixtieth system and roundgreek zero. Indians joined the principles of Greek numbering with a decimal multiplicative system taken from China. Also, they began to denote the numbers in one mark, as was customary in the ancient Indian numbering of Brahmi. Brilliant Seville translated this book to Latin, and the Indian account system was widely distributed throughout Europe.
Indian aged B. not later . At the same time, the concept was open and formalized. ( shunya ), which made it possible to go to .
Arab and Indo-Arabic figures are modified indian digits adapted to .
The Indian recording system has popularly popularized by scientist , author of the famous work " ", From the name of which the term happened" " Al-Khorezmi wrote a book "On Indian Account", contributing to popularization records numbers in the whole calipheat, right up to . contains the first mention and image of Arab numbers (except ) in . They appeared through in Spain, about 900 years.
Arabic figures became known in . Thanks to close connections ( ) I. ( ), ( from by ) had the opportunity to access scientific information, which no one had in the then . In particular, he one of the first among Europeans got acquainted with the Arabic figures, understood the convenience of their use compared to and began to promote their introduction into European science. IN al-Khorezmi's book "On Indian score" was transferred to the Latin language and played a very large role in the development of European arithmetic and the introduction of Indo-Arabic figures. The name "Arabic figures" was formed historically, due to the fact that the Arabs were distributed note. The figures that are used in Arab countries are very different from those used in European countries.
In the old Babylonian texts dating back 1700 to our era, there is no special sign denoting zero, for its designation, they simply left an empty place, more or less dedicated.
Arabic numbers (font without sneakers)
Writing numbers
Writing Arabic numbers consisted of segments of straight lines, where the number of corners corresponded to the magnitude of the sign. Probably, one of the Arab mathematicians once suggested the idea - to link the numeric value of the numbers with the number of corners in its writing.
Let's look at the Arabic numbers and see that
0 - Digit without a single angle in the draw.
1 - contains one sharp angle.
2 - contains two sharp corners.
3 - contains three sharp corners (correct, Arabic, drawing numbers is obtained when writing a number 3 when filling out the mail index on the envelope)
4 - contains 4 straight corners (this is explained by the presence of the "tail" at the bottom of the numbers, in no way affecting its recognition and identification)
5 - contains 5 straight corners (the purpose of the bottom tail is the same as the number 4 is the completion of the last angle)
6 - contains 6 straight corners.
7 - contains 7 straight and sharp corners (correct, Arabic, writing numbers 7 differs from the presence of a hyphena, crossing the vertical line in the middle at the right angle (remember how we write the figure 7), which gives 4 direct angle and 3 corners gives still upper broken line)
8 - contains 8 straight corners.
9 - contains 9 direct corners (this is explained by such an intricate bottom tail in the nine, which was supposed to complete 3 angle so that their total number was equal to 9.
In the modern world, we use Arabic figures. Since they are more convenient by writing. Their system is called ten times, 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 these numbers, we can write any number without limitation. Also thanks to zero, invented Muslims, writing has become much easier. Therefore, in our days, Arabic numbers are considered the most comfortable and simplest.
Also on the Internet, I found an interesting program translator numbers Titlo_0.12.2. You can find out in detail about it in the appendix.
Chapter 4.
Organization and conduct of research
The study was conducted among students of grade 5 and Internet survey (Appendix 1). A total of 30 people were interviewed.
Students and Internet users were offered 4 questions:
1. What figures do we use in the modern world?
2. Where did the numbers come to us?
3. Where did the concept of zero originate?
Research results:
Question 1: What figures we use in the modern world.
Looking at the chart, we see that most of the respondents are not mistaken and chose the correct answer. In the modern world, we use Arabic figures.Question 2: Where did the numbers come from us.
With the second question, the respondents did not cope. 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 the concept of zero originated.
On the third question, most of the respondents answered incorrectly, as Nul was invented in India. In the process of research, I noticed that the respondents were not confident in the right choice of a response.
Question 4:Using the table (Appendix 2) of writing numbers of different nations, write figures: 4, 10, 325, 543, on Egyptian (hieroglyphs), on Babylonian, in Greek, on Roman, in Slavic.
We coped with writing (out of 30 participants).
Slavssky
From this table we see that the most difficult writing of the numbers is Slavic. Also, the more signs increasing among the number, the more difficult it became to write it.
Conclusion
The purpose of my project it was found out the secret of the origin of Arabic numbers and the reason for their long-life. To achieve it, I had to solve the tasks. That's what came out of it.
Task number 1 - With the help of literary sources and the Internet, to get acquainted with the numbers of different nations. During the solution of this task, I met the numbers of ancient Egypt, Babylon, ancient Greece and Rome, did not bypass the Slavic Cyrillic numbering and, of course, Arabic numbers. I think within the framework of this project, the task has been solved by 100%. And it is very cool that work in this direction can be continued, because there are still many different numbering, both studied and not studied. In the future, I would like to explore the numbers of the Great Civilization of Maya.
Task # 2 - Find information on the origin of the Arabic figures. With this task, I also fully coped with the Internet and book N.Ya. Vilenkin "behind the pages of the textbook of mathematics." Indeed, the history of the Arabic figures was very confusing. I realized that I didn't quite correctly call our figures in Arabic. They concentrated the experience of many civilizations: both Egypt, and Babylonian, and Greek, and, of course, Indian. Yes, the Arabs added a lot of her to the Indian system, and it was the Arabs that distributed these numbers in Europe, but it would be unfair to consider them only to the Arab achievement.
Task # 3 - Compare different number systems to figure out why modern people use the Arabic figures. I believe that I managed to deal with this task. Unfortunately, I had to admit that our Slavic numbers are extremely uncomfortable in use. I imagine how modern schoolchildren in the letters and figures would be confused if we used to use Slavic numbering. The convenience of Arabic numbering is obvious:
arabic viewing system positioning, i.e. The value of the number depends on its place in the number of numbers, it presents the concept of "zero" and that is why with just ten digits we have the opportunity to record absolutely any number!
Task number 4 - explore the level of knowledge of the people around me about the numbers that they all use. This task was solved with the help of a survey of school students and the Internet survey. I found out that the majority of respondents know that we use the Arabic number system, but very few people have an idea of \u200b\u200bwhere our numbers come from, and where the concept of zero originates. With great difficulty, respondents recorded modern numbers in other surcharge systems. Moreover, the greatest difficulty caused a record of the number by Slavic numbers. Working in this direction, I made my personal little discovery - discovered the program - translator numbers (Titio._0.12.2).
Task number 5 - Creating a presentation, which would reflect the results of my design - research work - as well as solved.
I believe that I reached my goal and fulfilled all the tasks. My hypothesis was fully confirmed: the history of Arabic numbers is full of riddles, and the longevity of the Arabic number system is associated with its convenience. I really liked working with the project. In the future, I want to continue working in this direction, since now I was interested in the issue of magic numbers.
Magic numbers - the energy of God,
Mathematics letters
It is necessary to work for a very long time
To know your spirit.
glagolites and back. Also "Title" can translatefigures peoples: Chinese, Armenian, Georgian, Greek (Ionical and Attic), Roman, Jewish numbers, Mayan numbers and others.The ranges of numbers in the "Title" are small, but are quite sufficient for most needs of numismatists, philatelists and buquins when determining dates and denominations on coins, stamps and books. However, the historians-lovers of Title can also help.
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 - that of them are used, under which there is a check mark. All switching B.translator numbersyou can do with the already typed number - the changes are immediately displayed in the final window.
Ministry of Common and Vocational Education of the Sverdlovsk Region MOU SOSH №62
Direction: Scientific - technical
The secret of the occurrence of Arab numbers
Artists:
Nadyrshin Damir Rafaelievich
Chekasin Egor Romanovich
Leader: Kulchitskaya L.A.
Mathematics teacher WCC
MOU SOSH №62.
Ekaterinburg, 2011.
Introduction
Purpose of work:
1. Get acquainted with the figures of antiquity:
Arabic
Of different nations
Chinese
Devanagari.
Modern
2. Learn about the Arabic figures: their writing, history and development
3. Find out why Arabic numbers are more convenient than other number systems
We will get acquainted with the numbers of different nations and follow their development from antiquity, to the present day. We will learn why the Arabic number is the most convenient? How did the numbers look in antiquity? How did Chinese figures written? How and when did Europeans meet Arabic figures? Why is an uncomfortable system for the number of ancient Rome? You will learn the essay "The Secret of the Arabic Numbers"
1. Arabic numbers
1.1 The secret of the occurrence of Arab numbers
The traditional name of ten mathematical signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. With the help of them, any numbers are written along a decimal number system. For millennia, people used fingers to designate the number. So, one thing they, as well as we, showed one finger, three - three. With the help of the hand it was possible to show up to five units. To express a larger number, both hands were used, and in some cases both legs. Now we constantly use numbers. We use them to measure time, buy and sell, call on the phone, watch TV, drive a car. In addition, each person has different numbers identifying personally. For example, in the identity card, in a bank account, in a credit card, etc. Moreover, in the computer world all information, and this text, including, is transmitted by numerical codes.
We meet with numbers at every step and so they are accustomed to them that they almost do not pay a report, how important they play in our lives. The numbers make up part of human thinking. Throughout history, each people wrote numbers, considered and calculated with their help. The first written figures that we have reliable evidence appeared in Egypt and Mesopotamia about five thousand years ago. Although these two cultures were very far from each other, their numeric systems are very similar, as if they represent one method - using serifs on a tree or stone for recording past days. Egyptian priests wrote on a papyrus, and in Mesopotamia on soft clay. Of course, the specific forms of their numbers are different, but in the one, and in other cultures used simple dashs for units and other tags for tens and higher orders. In addition, in both systems, they wrote the desired figure, repeating the invasses and tags the desired number of times.
Two Egyptian documents were found, created about four thousand years ago, with the most ancient mathematical records from those discovered so far. It is worth noting that these are mathematical records, and not just numeric.
1.2 History
The story of our usual "Arab" numbers is very confused. It is impossible to say exactly and reliably as they occurred. One thing is exactly known that it is thanks to the ancient astronomers, namely, with their exact calculations we have our numbers. Between II and VI centuries AD. Indian astronomers became acquainted with Greek astronomy. They adopted the sixties and round Greek zero. Indians joined the principles of Greek numbering with a decimal multiplicative system taken from China. Also, they began to denote the numbers in one mark, as was customary in the ancient Indian numbering of Brahmi. Brilliant Seville translated this book to Latin, and the Indian account system was widely distributed throughout Europe.
The numbers arose in India, no later than the V century. Then the concept of zero (shunya) was opened and formalized. Arabic figures arose in India, no later than the V century. At the same time, the concept of zero was opened and formalized, which made it possible to proceed to the positional record. Which Arabic figures became known to Europeans in the x centuries. Thanks to the close relations of Christian Barcelona and Muslim Cordoba), Sylvester had the opportunity to access scientific information, which no one had in then Europe. In particular, he was one of the first among Europeans with Arabic figures, understood the convenience of their use compared to Roman and began to introduce them to European science.
In the old Babylonian texts dating back 1700 to our era, there is no special sign denoting zero, for its designation, they simply left an empty place, more or less dedicated.
1.3 Writing numbers
Writing Arabic numbers consisted of segments of straight lines, where the number of corners corresponded to the magnitude of the sign. Probably, one of the Arab mathematicians once suggested the idea - to link the numeric value of the numbers with the number of corners in its writing.
Let's look at the Arabic numbers and see that
0 - Digit without a single angle in the draw.
1 - contains one sharp angle.
2 - contains two sharp corners.
3 - contains three sharp corners (correct, Arabic, drawing numbers is obtained when writing a number 3 when filling out the mail index on the envelope)
4 - contains 4 straight corners (this is explained by the presence of the "tail" at the bottom of the numbers, in no way affecting its recognition and identification)
5 - contains 5 straight corners (the purpose of the bottom tail is the same as the number 4 is the completion of the last angle)
6 - contains 6 straight corners.
7 - contains 7 straight and sharp corners (correct, Arabic, writing numbers 7 differs from the presence of a hyphena, crossing the vertical line in the middle at the right angle (remember how we write the figure 7), which gives 4 direct angle and 3 corners gives still upper broken line)
8 - contains 8 straight corners.
9 - contains 9 direct corners (this is explained by such an intricate bottom tail in the nine, which was supposed to complete 3 angle so that their total number was equal to 9.
We learned when and how the Arab numbers appeared, as they say that they represent themselves and the general meaning of numbers
2. Figures of different peoples
Arabic figures used in African Arab countries
1 2 3 4 5 6 7 8 9 0
◗Indo - Arabic figures
٠١٢٣٤٥٦٧٨٩
◗yfras in the letter of the Outi.
୦୧୨୩୪୫୬୭୮୯
◗Syphras in a Tibetan letter.
༠༡༢༣༤༥༦༧༨༩
◗Syphras in Thai letter.
๐๑๒๓๔๕๖๗๘๙
◗yfras in the Lao letter.
໐໑໒໓໔໕໖໗໘໙
The Egyptians wrote hieroglyphs, numbers too. The Egyptians had signs to designate numbers from 1 to 10 and special hieroglyphs to designate tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions and even tens of millions. The next stage in the history of the number was carried out by ancient Romans. They invented a calculus system based on the use of letters to display numbers. They used in their system the letters "I", "V", "L", "C", "D", and "M". The letter had a different meaning, each figure corresponded to the position of the letter. In order to read the Roman digit or write it, you need to follow several basic rules.
In Central America in the first millennium, our Mayan era wrote any number using only three signs: point, line and ellipse. The point had a unit value, the line meant five, the combination of points and lines served to write numbers from one to nineteen. The ellipse under any of these signs increased its value in twenty times. Examples of figures of ancient Rome:
1 letters are written from left to right, starting from the most importance. For example, "XV" - 15, "DLV" - 555, "MCLI" - 1151.
2 letters "I", "X", "C", and "M" can be repeated to three times in a row. For example, "II" - 2, "XXX" - 30, "CC" - 200, "MMCCXXX" - 1230.
3 letters "V", "L" and "D" cannot be repeated.
4 Figures 4, 9, 40, 90 and 900 should be written, combining the letters "IV" - 4, "IX" - 9, "XL" - 40, "XC" - 90, "CD" - 400, "CM" - 900. For example, 48 is "XLVIII", 449 - "CDXLIX". The value of the left letter reduces the value of the right.
5 horizontal line over the letter increases its value to 1000
Due to the use of a small number of signs for writing, the numbers had to repeat the same sign many times, forming a long series of characters. In the documents of the Aztec officials, there are accounts that indicated the results of OPI and the calculations of the filters received by the Aztecs from the conquered cities. In these documents, you can see long rows of signs similar to the real hieroglyphs. In China, chopsticks from ivory or bamboo they denoted numbers from one to nine. The numbers from one to five were denoted by the amount of sticks, depending on the number. So, two sticks corresponded to the number two. And in order to specify the numbers from six to nine, one horizontal wand was placed in the top of the digit. For example, 6 resembled the letter "T". The diseases, or symbols of our numbers, have arabic origin. Arab culture, in turn, they were borrowed in India. The gap between the eighth and thirteenth centuries was one of the brilliant periods in the history of science in the Muslim world. Muslims had close connections with both Asian and European cultures. They were able to extract from them all the most outstanding. In India, they borrowed a calculus system and some mathematical signs.
711 - can be considered a year of opening Indian figures in the territories of the Middle East, in Europe, they, of course, got much later. Why exactly the Middle East? Well, a completely legitimate question. The fact is that the wonderful city of Bahda - or as we used to call him - Baghdad in those times was a rather attractive place for scientists. There were openly many scientific and pseudo-scientific schools, in which, nevertheless, was the exchange of knowledge gained and skills. In 711 there was a treatise about the stars and at the same time, about numbers. It is now difficult to say whether there were progressive views on the figures of the Indian scientist who submitted to the world an astronomical report, but here's the fact that in his help now we have the Arabic figures are truly not forgotten and deserves prempting thanks. At that time, in science, they used mainly three systems of calculating numbers: Roman, Greek and Egyptian - Persian. In principle, they were fairly convenient for the maintenance of a small farm to say one person, but it was very difficult to record large numbers, although the ancient Greek philosophers and mathematics called their score and records and records of the numbers almost perfect in the world. This by and large, of course, was not true.
This numbering was created to correspondence in the sacred books of Western Slavs. It was used infrequently, but long enough. By organization, it exactly repeats the Greek numbering. It was used from VIII to XIII century.
Numbers starting from large values \u200b\u200band ending with smaller, left to right. If tens, units, or some other discharge it was not, then they passed it
Such a record of the number is additive, that is, it uses only addition:
= 800+60+3 = 863
In order not to confuse letters and numbers, the title is used - horizontal dashes over numbers, or points.
Latin (Roman) numbering
This is probably the most famous numbering, after Arabic. With her, we often faced in everyday life. These are chapter numbers in books, indication of the century, numbers on the clock clock, etc.
This numbering appeared in ancient Rome. It was used for an additive alphabetical number system.
Before the sign M was portrayed by the sign f, because then 500 and began to portray the sign D as "half" F. The pair L and C, X and V were also built.
Numbers starting from large values \u200b\u200band ending with smaller, left to right. If the digit with a smaller value is recorded before the number with a large value, it happened to be subtracted.
CCXXXVII \u003d 100 + 100 + 10 + 10 + 10 + 5 + 1 + 1 \u003d 237
Xxxix \u003d 10 + 10 + 10-1 + 10 \u003d 39
There is a rule that cannot be recorded in a row 4 of the same numbers, such a combination is replaced by a combination with a deduction rule, for example:
Xxxx \u003d xc (50-10)
CCCC \u003d CD (500-100)
There is no significant information about the origin of Roman numbers. In Roman numbering, traces of a five-hour number system are clearly affected. In the language of the same traces there are no five traces. So, these figures were borrowed by the Romans among another people (most likely Etruscans).
Such a numbering prevailed in Italy until the XIII century, and in other countries of Western Europe - until the XVI century.
New, or Arabic Numbering
This is the most common numbering to date. The name "Arabic" is not entirely true for it, because even though they took it to Europe from Arab countries, but she was not native there too. The real homeland of this numbering is India.
In various parts of India, there were a variety of numbering systems, but at some point there were alone among them. In it, the figures had the appearance of the initial letters of the corresponding numerals in ancient Indian language - Sanskrit using the Alphabet "Devanagari".
Initially, these signs were the following numbers 1, 2, 3, ... 9, 10, 20, 30, ..., 90, 100, 1000; With their help, other numbers were recorded. But later, a special sign was introduced - a bold point, or a circle, to indicate the empty discharge; And the numbering "Devanagari" turned into a local decimal system. How and when such a transition was accomplished - it is still unknown. By the middle of the 6th century, the positional numbering system is widely used. At the same time, she penetrates the neighboring countries: Indochina, China, Tibet, Central Asia.
A decisive role in the distribution of Indian numbering in Arab countries was played by Mohammed Al Khorezmi in the early Ix century. It was translated in Western Europe to Latin in the XII century. In the XIII century, Indian numbering gets a predominance in Italy. In other countries, it applies to the XVI century. Europeans, borrowing the numbering from Arabs, called it "Arab". This is a historically incorrect name is held and understood.
The word "figure" (in Arabic "Sofr") is borrowed from Arabic (in Arabic "), meaning literally" empty place "(the translation of Sunshi's Sunskrit, having the same meaning). This word was used to name a blank discharge sign, and this meaning kept until the XVIII century, although in the XV century the Latin term "zero" appeared (Nullum - nothing).
The form of Indian numbers has undergone diverse changes. That form we use now installed in the XVI century.
Arabic numerals.Arabic numbers - the traditional name of the set of ten signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; It is now used in most countries to record numbers in a decimal number system.
History
Arabic numerals. Figures 4, 5 and 6 exist in two versions, on the left - Arabic, right - Persian.
Indian numbers arose in India, no later than the V century. At the same time, the concept of zero was opened and formalized, which made it possible to move to the secret of the occurrence of Arab numbers
The traditional name of ten mathematical signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. With the help of them, any numbers are written along a decimal number system. For millennia, people used fingers to designate the number. So, one thing they, as well as we, showed one finger, three - three. With the help of the hand it was possible to show up to five units. To express a larger number, both hands were used, and in some cases both legs. Now we constantly use numbers. We use them to measure time, buy and sell, call on the phone, watch TV, drive a car. In addition, each person has different numbers identifying personally. For example, in the identity card, in a bank account, in a credit card, etc. Moreover, in the computer world all information, and this text, including, is transmitted by numerical codes.
We meet with numbers at every step and so they are accustomed to them that they almost do not pay a report, how important they play in our lives. The numbers make up part of human thinking. Throughout history, each people wrote numbers, considered and calculated with their help. The first written figures that we have reliable evidence appeared in Egypt and Mesopotamia about five thousand years ago. Although these two cultures were very far from each other, their numeric systems are very similar, as if they represent one method - using serifs on a tree or stone for recording past days. Egyptian priests wrote on a papyrus, and in Mesopotamia on soft clay. Of course, the specific forms of their numbers are different, but in the one, and in other cultures used simple dashs for units and other tags for tens and higher orders. In addition, in both systems, they wrote the desired figure, repeating the invasses and tags the desired number of times.
Two Egyptian documents were found, created about four thousand years ago, with the most ancient mathematical records from those discovered so far. It is worth noting that these are mathematical records, and not just numeric.
1.2 History
The story of our usual "Arab" numbers is very confused. It is impossible to say exactly and reliably as they occurred. One thing is exactly known that it is thanks to the ancient astronomers, namely, with their exact calculations we have our numbers. Between II and VI centuries AD. Indian astronomers became acquainted with Greek astronomy. They adopted the sixties and round Greek zero. Indians joined the principles of Greek numbering with a decimal multiplicative system taken from China. Also, they began to denote the numbers in one mark, as was customary in the ancient Indian numbering of Brahmi. Brilliant Seville translated this book to Latin, and the Indian account system was widely distributed throughout Europe.
The numbers arose in India, no later than the V century. Then the concept of zero (shunya) was opened and formalized. Arabic figures arose in India, no later than the V century. At the same time, the concept of zero was opened and formalized, which made it possible to proceed to the positional record. Which Arabic figures became known to Europeans in the x centuries. Thanks to the close relations of Christian Barcelona and Muslim Cordoba), Sylvester had the opportunity to access scientific information, which no one had in then Europe. In particular, he was one of the first among Europeans with Arabic figures, understood the convenience of their use compared to Roman and began to introduce them to European science.
In the old Babylonian texts dating back 1700 to our era, there is no special sign denoting zero, for its designation, they simply left an empty place, more or less dedicated.
1.3 Writing numbers
Writing Arabic numbers consisted of segments of straight lines, where the number of corners corresponded to the magnitude of the sign. Probably, one of the Arab mathematicians once suggested the idea - to link the numeric value of the numbers with the number of corners in its writing.
Let's look at the Arabic numbers and see that
0 - Digit without a single angle in the draw.
1 - contains one sharp angle.
2 - contains two sharp corners.
3 - contains three sharp corners (correct, Arabic, drawing numbers is obtained when writing a number 3 when filling out the mail index on the envelope)
4 - contains 4 straight corners (this is explained by the presence of the "tail" at the bottom of the numbers, in no way affecting its recognition and identification)
5 - contains 5 straight corners (the purpose of the bottom tail is the same as the number 4 is the completion of the last angle)
6 - contains 6 straight corners.
7 - contains 7 straight and sharp corners (correct, Arabic, writing numbers 7 differs from the presence of a hyphena, crossing the vertical line in the middle at the right angle (remember how we write the figure 7), which gives 4 direct angle and 3 corners gives still upper broken line)
8 - contains 8 straight corners.
9 - contains 9 direct corners (this is explained by such an intricate bottom tail in the nine, which was supposed to complete 3 angle so that their total number was equal to 9.
Output
We learned when and how the Arab numbers appeared, as they say that they represent themselves and the general meaning of numbers
2. Figures of different peoples
Arabic figures used in African Arab countries
1 2 3 4 5 6 7 8 9 0
◗ Indo - Arabic figures
٠١٢٣٤٥٦٧٨٩
◗ Figures in the letter of the Ouri.
୦୧୨୩୪୫୬୭୮୯
◗ Figures in a Tibetan letter.
༠༡༢༣༤༥༦༧༨༩
◗ Figures in Thai letter.
๐๑๒๓๔๕๖๗๘๙
◗ Figures in the Lao letter.
໐໑໒໓໔໕໖໗໘໙
The Egyptians wrote hieroglyphs, numbers too. The Egyptians had signs to designate numbers from 1 to 10 and special hieroglyphs to designate tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions and even tens of millions. The next stage in the history of the number was carried out by ancient Romans. They invented a calculus system based on the use of letters to display numbers. They used in their system the letters "I", "V", "L", "C", "D", and "M". The letter had a different meaning, each figure corresponded to the position of the letter. In order to read the Roman digit or write it, you need to follow several basic rules.
In Central America in the first millennium, our Mayan era wrote any number using only three signs: point, line and ellipse. The point had a unit value, the line meant five, the combination of points and lines served to write numbers from one to nineteen. The ellipse under any of these signs increased its value in twenty times. Examples of figures of ancient Rome:
1 letters are written from left to right, starting from the most importance. For example, "XV" - 15, "DLV" - 555, "MCLI" - 1151.
2 letters "I", "X", "C", and "M" can be repeated to three times in a row. For example, "II" - 2, "XXX" - 30, "CC" - 200, "MMCCXXX" - 1230.
3 letters "V", "L" and "D" cannot be repeated.
4 Figures 4, 9, 40, 90 and 900 should be written, combining the letters "IV" - 4, "IX" - 9, "XL" - 40, "XC" - 90, "CD" - 400, "CM" - 900. For example, 48 is "XLVIII", 449 - "CDXLIX". The value of the left letter reduces the value of the right.
5 horizontal line over the letter increases its value to 1000
Due to the use of a small number of signs for writing, the numbers had to repeat the same sign many times, forming a long series of characters. In the documents of the Aztec officials, there are accounts that indicated the results of OPI and the calculations of the filters received by the Aztecs from the conquered cities. In these documents, you can see long rows of signs similar to the real hieroglyphs. In China, chopsticks from ivory or bamboo they denoted numbers from one to nine. The numbers from one to five were denoted by the amount of sticks, depending on the number. So, two sticks corresponded to the number two. And in order to specify the numbers from six to nine, one horizontal wand was placed in the top of the digit. For example, 6 resembled the letter "T". The diseases, or symbols of our numbers, have arabic origin. Arab culture, in turn, they were borrowed in India. The gap between the eighth and thirteenth centuries was one of the brilliant periods in the history of science in the Muslim world. Muslims had close connections with both Asian and European cultures. They were able to extract from them all the most outstanding. In India, they borrowed a calculus system and some mathematical signs.
711 - can be considered a year of opening Indian figures in the territories of the Middle East, in Europe, they, of course, got much later. Why exactly the Middle East? Well, a completely legitimate question. The fact is that the wonderful city of Bahda - or as we used to call him - Baghdad in those times was a rather attractive place for scientists. There were openly many scientific and pseudo-scientific schools, in which, nevertheless, was the exchange of knowledge gained and skills. In 711 there was a treatise about the stars and at the same time, about numbers. It is now difficult to say whether there were progressive views on the figures of the Indian scientist who submitted to the world an astronomical report, but here's the fact that in his help now we have the Arabic figures are truly not forgotten and deserves prempting thanks. At that time, in science, they used mainly three systems of calculating numbers: Roman, Greek and Egyptian - Persian. In principle, they were fairly convenient for the maintenance of a small farm to say one person, but it was very difficult to record large numbers, although the ancient Greek philosophers and mathematics called their score and records and records of the numbers almost perfect in the world. This by and large, of course, was not true.
The method invented by Indians and brought to the world of Arabs was a more convenient and economical, so it was possible to save not only resources for the letter (whether papyrus, paper or even something else) but also their own time, which people at all times Catastrophic lacked. Over time, the corners are smoothed, and the figures acquired the usual look. For many centuries, the whole world has enjoyed the Arab number of numbers. With these ten icons, you can easily express tremendous values. By the way, the word "digit" is also Arabic. Arab mathematicians transferred the Indian word "Sunya" in meaning to his language. Instead of "Sunya", they began to say "SIFR" or "digits", and this is already familiar to us.