Who invented Arabic? Abstract: The secret of the origin of Arabic numbers
Mathematics, along with philosophy, is a fundamental discipline on the basis of which applied sciences were created, which gave us space flights, complex operations with the human body, communication via radio and electromagnetic waves, and much more. Since ancient times, mathematics as such has developed, starting with the most primitive calculations of livestock heads using notches and sticks, and increasing to the complex level of astronomical calculations and the creation of functional mechanisms. One of the important aspects of the development of mathematics was the counting system. After all, a lot depends on it: from the convenience of writing large numbers, to some revolutionary concepts that Arabic numerals introduced. But this will be discussed below.
Origin of Arabic numerals
It would seem that there is no intrigue here, and the answer is already in the title. Well, what is there to think about, what people invented Arabic numerals? Of course Arabs! However, not everything is as simple as it seems at first glance. Today we call them that because it was the Arabs who introduced Europeans to such recordings. In the Middle Ages, this people also gave the world many outstanding scientists, thinkers and poets. However, they were not the ones who created Arabic numerals. The history of this calculation is much older than the Arab civilization itself, and it lies further in the East, in India. It was here, in a mysterious land that has always been shrouded in the West in an aura of fabulousness and fantasy, that Arabic numerals were invented. It is not known exactly when exactly this happened, but it has been proven that no later than the 5th century AD. In this country they first began to be used, and only several centuries later a convenient recording system was borrowed by the mathematicians of the Caliphate. In this state they were first popularized by the scientist al-Khwarizmi in the first half of the 9th century. Initially, Indian numerals had angular shapes. According to one version, each of them had the same number of angles as they nominally indicated. This can be easily seen in the first figure. However, over time, the need to adhere to a strict number of angles disappeared. And among the Arabs, they were completely adapted to the local script and acquired rounded shapes. The new popular notation of calculus began to rapidly conquer the Muslim world. And already around the year 900, the Spaniards first became acquainted with it through the Pyrenean Moors. The close ties between Christian Barcelona and Arab Cordoba contributed to the speedy adoption of the convenient system by Europeans. And soon Indian numbers conquered the entire continent.
To date, the Indian recording system has replaced almost all of its once competing systems. The Arabs, who wrote alphabetic meanings before her, abandoned this method. Roman numerals are still used, but rather as a tribute to tradition in some notations. Arabic numerals have completely gained serious positions. In addition to the fact that the system is simply convenient because it contains only ten digits - from zero to nine, it is also laconic. However, the most important concept that came to Europe with Indian numerals is the concept of zero, which made it possible to denote what is not there.
Known as "Arabic", these are modified forms of Indian numerals and were introduced by Al-Khawarizmi. There are two sets of numbers based on Indian characters. One of them was used in the eastern part of the Muslim world and is known as "Indo-Arabic numerals", or simply "Indian numerals". The other (“Gubbaria”) became widespread in the western part of the Muslim world, from where it came to Europe and became known as “Arabic numerals,” gradually taking on its modern form.
Western Arabic numbers were called “gubbariyya”, since the Arabs used a counting board covered with dust (in Arabic “gubar” - “dust”). People wrote with a finger or some other object on a surface with a thin layer of dust or sand, and then erased it.
The number “zero” was initially not oval, but round. The circle was chosen to convert the Indian symbols for zero since it has no angles (the number of angles is zero).
The Indians called zero "sunya" — "empty". The Arabs translated it with the word that the number of angles is “as-syfr”, which is where the word “digit” comes from (as well as the word “cipher”). The word corresponded to their “digit” (Latin - “ciffra") in European literature originally meant zero, and then 0 began to be called the Latin word "null" (that is, "no"), and the word "digit" is all the signs from 0 to 9. In Latin manuscripts of the 12-13th centuries. zero is also calledcircullus (“circle”),nihil ("nothing") orfiguranihili (“nothing sign”).
You might like it
Muslims remember the blessed water of ZamZam when talking about the Hajj, as well as during illness or any difficulty. Allah Almighty created this water special, and it serves to heal and bless people.
According to legend, the source of Zam-Zam appeared as follows:
When, by the command of Allah, Prophet Ibrahim, peace be upon him, with Hajar and his son Ismail arrived at the territory of the future city of Mecca, there were no inhabitants there. Allah Almighty gave Ibrahim the Revelation to leave his family there. Prophet Ibrahim, peace be upon Him, fulfilled what the Creator commanded Him, left Hajar and his son with a vessel of water and left. After the water ran out, little Isma'il began to cry, and His mother began to look for water. She climbed one hill, which is called Safa, and then moved to another hill - Marua. So she walked between them seven times. Allah Almighty saved them by creating the Zam-Zam spring for them.
The word "Zam-Zam" has many meanings, one of which is "sandwiched among the sands." The sacred spring is located next to the Banu Shaiba gate, 18 meters from the Black Stone, not far from the Safa and Marua hills.
Prophet Muhammad in the name of the Prophet "Muhammad" the letter "x" is pronounced like ح in Arabic, peace be upon Him, taught that Zam-Zam is the best water on earth, it strengthens the heart and calms in fear. If you drink ZamZam water with the intention of healing, then by the Will of Allah the person will recover. If someone is thirsty or hungry, then drinking this water with a specific intention will quench his thirst and be full. And if, while drinking, you turn to Allah with some other request, then by the Will of Allah what you want will be received.
Numerous scientific studies have confirmed that Zam-Zam water contains a large number of microelements beneficial to the human body. Among them: calcium, magnesium, fluorides. In addition, water has a constant, unchanging salt composition and taste. It can be stored for years without changing its properties. Nowadays, the composition and taste of Zam-Zam water is the same as it was at the time when the source first appeared. There are no pathogenic microbes in ZamZam water, despite the fact that the water has not been chemically treated or chlorinated. The ZamZam spring never dries up, it is always full of water, despite the fact that other springs in the vicinity of Mecca periodically dry up, and some have disappeared altogether.
For a long time, researchers could not establish where the water in the source came from, but then it turned out that the water flows into the source evenly along the entire perimeter of the pool.
World-famous Japanese researcher Dr. Masaru Emoto, who heads a research institute in Tokyo, claims that Zam Zam water has properties that are not found in ordinary water. The researcher was surprised not only by the unique properties of Zamzam water, but also by the fact that the scientific experiments he conducted using nanotechnology could not change them. And also the fact that one drop of sacred water added to 1000 drops of plain water changes the properties of ordinary water to the properties of “Zamzam”.
Dr. Emoto said that he received Zam Zam water from an Arab who lived in Japan. He began to examine it and realized that Zam Zam water is the only water that is not similar in its crystals to any water on earth, no matter where it comes from. Along with this, after each repeated experiment, the crystals of this water showed new and unusual species, which proved that this water is not simple.
A Japanese researcher, who is the founder of a number of theories, discovered the amazing phenomenon that crystals of ordinary water change their properties when “Basmalyah” is read on it, i.e. expressions “Bismillah hir-Rah ma nir-Rahi m.” He confirmed that the words that Muslims say before starting all their business, before eating and before going to bed have an amazing effect on water crystals, and they are transformed into extraordinary beauty. The same beneficial changes occur with water if you play an audio recording of the Holy Quran near it. And when they read one of the 99 most beautiful names of Allah “Al-‘Alim” (the All-Knowing), the water crystals transformed into something amazing, which indicates the greatness of the names of the Almighty.
Another scientist named Mazrugiy commented on the research of Dr. Masaro Emoto, who also observed improvement in water when dua was read on it. And he added that after this one can imagine the effect of prayer or reading the Kurtan on a person who is 70% water.
In our store you can buy it brought from Mecca, undiluted, in its pure form.
“[Truly] Allah is the Creator of the earth and the Lord of the worlds. He raised firmly standing mountains above the earth [so that it would not shake]. He blessed the earth with water, plants, trees and fruits<…>. He made the heavens perfect<…>and decorated the lower sky with luminaries<…>And all this was created exactly as Almighty and All-Knowing Allah wanted.” The meaning of verses 9-16 of Surah Fussylat
One of God's most fascinating creations is the mountains. They amaze with their splendor and grandeur. Near the mountains that rise up, we feel like tiny creatures and are even more convinced of the Omnipotence of the Creator.
The amazing thing is that the strong and massive mountains are not just a mound of rock on the ground! This is confirmed by the latest geological research, but about 1500 years ago the Prophet Muhammad conveyed to people the verses of the Holy Qur'an, which clearly stated that the mountain in fact also goes deep underground and has a “root”.
It is said in the Holy Quran (1): “Don’t they see evidence of the Omnipotence of Allah: the earth, comfortable for life, like a cradle for a baby, and the mountains going deep and serving as supports so that it does not fall apart?!”
This verse says that mountains are driven deep into the earth like piles - they strengthen and hold it. Theologians explained that the depth of the mountains inside the earth is 2 times or more greater than their height above the earth!
And another verse of the Holy Quran (2) says: “And don’t they see the mountains that are erected firmly and do not shake, despite their enormous height?!” Thus, mountains strengthen the earth, just as stakes driven into the soil support a tent. The interpretation of another verse of the Holy Quran (3) says that mountains strengthen the earth, just as an anchor holds a ship.
Mountains not only serve as earth supports, but also keep the earth from shaking. The Holy Quran (Surah An-Nahl, verse 15) says: “Allah has established firmly standing mountains on the earth so that it does not shake.” And some modern geological theories confirm that mountains are stabilizing elements of the earth, and not just “folds of the earth’s crust.”
It is reported that when Allah created the earth, it moved. Seeing this, the angels were surprised: “Can anyone live on it?!” And then Allah created mountains that stopped the earth. It was so amazing that the Angels did not even know what they were made of.
Prophet Muhammad told people that at the End of the World the mountains would be destroyed. It is said in verse 20 of Sura 78 “An-Naba’” meaning that at the End of the World the mountains will disappear like a mirage.
And it is also said in the Holy Quran (Surah Al-Kari'a, verses 4-5) meaning: “On that day people will be like scattered moths, and the mountains will be like torn wool.” That is, the mountains will turn to dust and scatter.
The same is said in verse 88 of Surah An-Naml: meaning: “[At the End of the World] you will see how the mountains, which you considered solid and unshakable, move quickly, like clouds.”
_____________________________
1 meaning of verses 6-7 of Surah An-Naba’
2 meaning of verse 19 of Surah Al-Gashiya
3 meaning of verse 32 of Surah An-Nazi'at
Everything that makes a state great and prosperous, everything that is aimed at perfection and civilization, could be found in Muslim Spain. The Islamic rulers of Al-Andaluz encouraged the development of science and the arts, establishing many scientific centers in which scientists from Europe, Africa and the Middle East came to work and study. Al-Andaluz became a center of civilization and education, where world-famous scientists worked.
One of the first scholars of Al-Andaluz was ‘Abbas ibn Farnas. Like many scientists of that time, he studied various sciences, but most of all he was interested in mechanics. In 880 he designed the first flying machine. Ibn Firnas also developed a new model of a water clock and a certain analogue of a metronome, found a way to make colorless glass, developed various kinds of glass planispheres, made corrective lenses (the so-called 'reading stones'), found a way to cut crystals, invented a system of rings suitable to depict the movement of stars and planets.
Scientists of Islamic Spain made great contributions to the development of mathematics and astronomy. The most prominent mathematician and astronomer of Al-Andaluz in the 10th century was Abul-Qasim Maslama ibn Ahmad Al-Majritiya (Maslama of Madrid) (c. 940-1008).
He wrote a number of books on astronomy and mathematics, worked a lot on the study and Arabic translation of Ptolemy's Almagest, expanded and corrected the astronomical tables of the famous scientist Al-Khawarizmi. He also compiled conversion tables in which the dates of the Persian calendar were correlated with the dates of the Hijri in such a way that events from the history of Persia were accurately dated for the first time. In addition, Maslama Al-Majritiya developed new geodetic methods, and also wrote a book about the economy of Al-Andaluz. Not only was he an outstanding scientist himself, but he also founded a school of astronomy and mathematics, which marked the beginning of organized scientific research in Al-Andaluz.
Ibrahim ibn Yahya An-Na kka w Az-Zarqaliy (1029-1087), known in the West as Arzakel, was a leading mathematician and astronomer of Al-Andaluz in the 11th century. He surpassed other scientists in developing accurate astronomical instruments and designed a water clock that could determine the hours of day and night, as well as showing the days of the lunar months. He made a significant contribution to the compilation of the famous Toledo Tables - a highly accurate systematization of astronomical data. Az-Zarqaliy is also known for his “Book of Tables”, which made it possible to determine the days according to different calendars, as well as the position of the planets at any necessary time.
Scientists in Muslim Spain also made significant contributions to the development of medicine. One of the most famous doctors of Al-Andaluz was Abul-Qasim Az-Zahr aw y (963-1013). His greatest achievements are associated with surgery. He compiled the famous 30-volume medical encyclopedia Al-Tasrif, covering various aspects of medical science. The most important part of this encyclopedia consists of three books on surgery. This encyclopedia was later translated into Latin and used by physicians throughout Europe. Al-Zahrawiy is also known for having invented a number of surgical instruments. He was also an expert in the field of dentistry. Another invention of Az-Zahrawiy is a solid lipstick based on wax, flavors and dyes. Also, such famous Andalusian scientists as Muhammad ibn Ahmad ibn Rushd (Averroes)(1126-1198) - author of the medical encyclopedia "Kulliyat"; ‘Abdul-Malik ibn Dhuhr (Avenzoar)(1072-1162) - hereditary doctor, author of books on nutrition, dietology and hygiene; (1313-1374) - author of a book on the theory of infectious diseases; Muhammad ibn Zakariya Ar-Raziy(864-925) - author of medical encyclopedias, who was the first to use plaster casts and cotton wool, was an expert in the organization of hospitals and introduced the compilation of medical histories into medical practice. Andalusian doctors also paid attention to ethics and hygiene in medicine. Scientists noted that moral qualities are mandatory for a doctor - he must be sensitive, compassionate, able to withstand harsh criticism, and the doctor must also be clean and behave with dignity.
An important area of study in Al-Andalus was geography. Ahmad ibn Muhammad Ar-Raziy wrote a book on the general geography of Al-Andaluz, Muhammad ibn Yusuf Al-Warraq described the topography of North Africa, and ‘Abdullahh Al-Bakriy (1014- 1094) wrote an encyclopedic reference book of the countries of the world, which included history, descriptions of traditions, climate, largest cities, and even short entertaining stories. Famous travelers also made a great contribution to the development of geography: Muhammad ibn Ahmad ibn Jubair(1145-1217), who described his travels in travel diaries, and a famous cartographer Muhammad Al-Idrisiy(1100-1165).
Al-Andaluz scholars also made great contributions to the study of history. Muhammad Lisanud-Din ibn Al-Khatib wrote works Narrative of the History of Granada and History of Muslim Spain, which are important sources on the history of Muslim Spain. A ' Abdurra X m A n ibn Khaldun became famous as the author of the work “The Book of Instructive Examples on the History of the Arabs, Persians and Berbers and their contemporaries who had great power.” Andalusian scientists also developed such sciences as linguistics, sociology, social science, economics, etc. The list of scientific achievements of Muslim scientists in Spain is huge. They developed and introduced many technological innovations in such areas as metal processing, weaving, construction, agriculture and many others.
Writing existed in ancient India for a very long time. The age of the first tablets with images that were found on the territory of Ancient India is more than 4000 years. Scientists believe that behind the signs on these tablets there is a real language. By the way, this language has not yet been deciphered. And for 130 years now, scientists have been trying to decipher this language. It was possible to find out that numerous squares, rectangles, and jagged patterns are not pictograms with unique meanings, but rather a language system. The signs used in writing are very diverse, and this makes deciphering difficult.
The first tablets on which they wrote Ancient India were made of clay and written on them with a hard wooden stick. Many of the inscriptions found were made on stones, and "wrote" on them using a chisel. They also wrote on uncured clay, then fired the clay.
But most often, the talipot palm leaf, dried, softened, cut and divided into strips, was used as a writing material. For a book, several such strips were connected, which were tied together with twine threaded into a hole made in the center of the sheet or, if the volume was large, into two holes located at both ends. The book, as a rule, had a wooden cover, varnished and painted. In the Himalaya region, where it was difficult to obtain dry palm leaves, they were replaced with birch bark, which, properly processed and softened, was quite suitable for this. Along with these materials, cotton or silk, as well as thin sheets of wood or bamboo, were used. Documents were engraved on copper sheets.
In most of India, ink was obtained from black soot or charcoal, and writing was done with a reed pen. In the south, letters were generally written on palm leaves using a sharp stick, and the leaf was then sprinkled with a thin layer of black soot. This method gave a clear and precise outline of the letters and made it possible to write very finely.
The numbers we use today are called Arabic. Arabic numerals are ten mathematical symbols with which any numbers are written. They look like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These numbers appeared in Europe in the 10th–13th centuries. Today, most countries use Arabic numerals to write numbers used in the decimal system. It is believed that Arabic numerals came to us from India. They are modified Indian numerals.
The Indian recording system was created and widely popularized by the famous Arab scholar Al-Khwarizmi. He was the author of the treatise “Kitab al-jabr wa-al-muqabala”. It is from the name of this treatise that the word comes "algebra", which has become not just a term, but a science, without which it is impossible to imagine our life. The rules for performing arithmetic operations on integers and simple fractions in the decimal number system were first formulated by an outstanding medieval scientist named Muhammad ibn Musa al-Khorezmi (translated from Arabic this means “Muhammad, son of Musa from Khorezm, abbreviated Al-Khorezmi. Al- Khorezmi lived and worked in the 9th century. The Arabic original of his arithmetic work is lost, but there is a Latin translation of the 12th century, according to which Western Europe became acquainted with the decimal positional number system and the rules for performing arithmetic operations in it. Al Khorezmi sought to ensure that the rules he formulated were understandable to all literate people. It was very difficult to achieve this in a century when mathematical symbols (operation signs, brackets, letter symbols, etc.) had not yet been developed. But Al-Khorezmi managed to develop such a clear style in his works , a strict verbal instruction that did not give the reader any opportunity to evade the prescribed or skip any actions. In the Latin translation of Al-Khwarizmi’s book, the rules began with the words “Algorizmi said.” Over time, people forgot that “Algorism” is the author of the rules, and they began to call these rules themselves algorithms. Gradually, “Algorism said” was transformed into “the algorithm says.” Thus, the word “algorithm” comes from the name of the scientist Al-Khwarizmi. As a scientific term, it originally denoted only the rules for performing actions in the decimal number system. Over time, this word acquired a broader meaning and began to mean any rules of action. Currently, the word “algorithm” is one of the most important concepts in computer science.
The path of Arabic numerals to Europe
The origin of Arabic numerals in Europe is due to the fact that two states peacefully coexisted on the territory of modern Spain - the Christian County of Barcelona and the Muslim Caliphate of Cordoba. Sylvester II, who was Pope of the Christian Church from 999 to 1003, was an unusually educated man and an extraordinary scientist. He managed to reveal to Europeans the achievements of the Arabs in astronomy and mathematics. While still a simple monk, he gained access to Arabic scientific books and treatises. Sylvester II turned his attention to the ease of use of Arabic numerals and began to intensively promote them in Europe. This extraordinary man immediately drew his attention to the significant advantages that Arabic numerals have over Roman numerals, which were widely used in Europe at that time.
Residents of European countries did not immediately appreciate the enormous scientific significance of this knowledge. It took three centuries for these numbers to come into use and gain universal recognition. But after Arabic numerals took their place in medieval Europe, the Renaissance began. Thanks to the introduction of Arabic numerals, mathematics and physics, astronomy and geography began to develop. European science received a new serious impetus in its further development.
This page contains beautiful Arabic numerals, which cannot be typed from the keyboard. They can be copied and pasted where the font cannot be changed (on social networks). In addition to the numbers that Europeans use, there are also real ones - those that the Arabs themselves use. And for the kit, let them lie there and Roman numerals and Indian. They won’t ask for food, I hope. They are all from Unicode, you can find out more about them by entering them into the search on the site.
Arabic:
① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳
❶ ❷ ❸ ❹ ❺ ❻ ❼ ❽ ❾ ❿ ⓫ ⓬ ⓭ ⓮ ⓯ ⓰ ⓱ ⓲ ⓳ ⓴ ⓿ ❶ ❷ ❸ ❹ ❺ ❻ ❼ ❽ ❾ ❿
⓵ ⓶ ⓷ ⓸ ⓹ ⓺ ⓻ ⓼ ⓽ ⓾
¼ ½ ¾ ⅐ ⅑ ⅒ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ ⅟
⑴ ⑵ ⑶ ⑷ ⑸ ⑹ ⑺ ⑻ ⑼ ⑽ ⑾ ⑿ ⒀ ⒁ ⒂ ⒃ ⒄ ⒅ ⒆ ⒇
⒈ ⒉ ⒊ ⒋ ⒌ ⒍ ⒎ ⒏ ⒐ ⒑ ⒒ ⒓ ⒔ ⒕ ⒖ ⒗ ⒘ ⒙ ⒚ ⒛
𝟎 𝟏 𝟐 𝟑 𝟒 𝟓 𝟔 𝟕 𝟖 𝟗 𝟘 𝟙 𝟚 𝟛 𝟜 𝟝 𝟞 𝟟 𝟠 𝟡 𝟢 𝟣 𝟤 𝟥 𝟦 𝟧 𝟨 𝟩 𝟪 𝟫 𝟬 𝟭 𝟮 𝟯 𝟰 𝟱 𝟲 𝟳 𝟴 𝟵 𝟶 𝟷 𝟸 𝟹 𝟺 𝟻 𝟼 𝟽 𝟾 𝟿
Roman:
Ⅰ – 1 ; ⅩⅠ - 11
Ⅱ – 2 ; ⅩⅡ - 12
Ⅲ – 3 ; ⅩⅢ - 13
Ⅳ – 4 ; ⅩⅣ - 14
Ⅴ – 5 ; ⅩⅤ - 15
Ⅵ – 6 ; ⅩⅥ - 16
Ⅶ – 7 ; ⅩⅦ - 17
Ⅷ – 8 ; ⅩⅧ - 18
Ⅸ – 9 ; ⅩⅨ - 19
Ⅹ – 10 ; ⅩⅩ - 20
Ⅽ – 50 ; ⅩⅩⅠ - 21
Arabic for Arabs = Indian in Devanagari script = understandable to us
A little history. It is believed that the Arabic number system originated in India around the 5th century. Although, it is possible that even earlier in Babylon. Arabic numbers are called because they came to Europe from the Arabs. First, in the Muslim part of Spain, and in the 10th century, Pope Sylvester II also called for the abandonment of the cumbersome Latin notation. A serious impetus for the dissemination of Arabic numerals was the translation into Latin of Al-Khorezmi’s book “On Indian Accounting”.
The Hindu-Arabic number system is decimal. Any number is made up of 10 characters. Unicode, by the way, uses hexadecimal numbers. It is more convenient than the Roman one because it is positional. In such systems, the value that a digit denotes depends on its position in the number. In the number 90, the number 9 means ninety, and in the number 951, nine hundred. In non-positional systems, the location of the symbol does not play such a role. The Roman X means ten in both the number XII and the number MXC. Many peoples wrote numbers in a similar non-positional way. Among the Greeks and Slavs, some letters of the alphabet also had a numerical value.
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). Notation 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.
