The life and work of Muhammad al-Khwarizmi. All elementary mathematics - secondary mathematical Internet school - great mathematicians - al khorezmi

Biography of Al-Khwarizmi (full name - Abu Abdullah Muhammad ibn Musa al-Khwarizmi) (arab. ابو عبدالله محمد ابن موسى الخوارزمي IX century; Abdullah's father, Muhammad, son of Musa, a native of Khorezm and) Arab born Abdullah, astronomer, mathematician. There is very little information about the life of the scientist. Al-Khwarizmi (full name - Abu Abdullah Muhammad ibn Musa al-Khwarizmi) (arab. ابو عبدالله محمد ابن موسى الخوارزمي; father of Abdullah, Muhammad, astronomer of Musa, native, Khorezm and) Arab mathematician of the IX century and) There is very little information about the life of the scientist.

The founder of algebra It is generally accepted that the founder of algebra is Abu Jafar Muhammad ibn Musa al-Khwarizmi, who was born approximately in 786. Some historians argue that his name may indicate that he was from the Khorezm region, located in Central Asia south of the Aral Sea. It is generally accepted that the founder of algebra is Abu Jafar Muhammad ibn Musa al-Khwarizmi, who was born around 786. A number of historians argue that his name may indicate that he was from the Khorezm region, located in Central Asia south of the Aral Sea. seas.

Under Caliph al-Mamun (813833), al-Khwarizmi headed the library of the "House of Wisdom" in Baghdad, a kind of Academy. Under Caliph al-Vasik (842847), al-Khwarizmi led an expedition to the Khazars. The last mention of al-Khwarizmi dates back to 847. Under Caliph al-Mamun (813833), al-Khwarizmi headed the library of the "House of Wisdom" in Baghdad, a kind of Academy. Under Caliph al-Vasik (842847), al-Khwarizmi led an expedition to the Khazars. The last mention of al-Khorezmi refers to 847.

The "House of Wisdom" Al-Khwarizmi and his colleague Banu Musa were among the scholars of the "House of Wisdom" in Baghdad. In this academy, they translated Greek scientific manuscripts, studied and wrote essays on algebra, geometry and astronomy. Al-Khwarizmi, who was patronized by Al-Mamun, dedicated two of his works to the Caliph. Al-Khwarizmi and his colleague Banu Musa were among the scholars of the "House of Wisdom" in Baghdad. In this academy, they translated Greek scientific manuscripts, studied and wrote essays on algebra, geometry and astronomy. Al-Khwarizmi, who was patronized by Al-Mamun, dedicated two of his works to the Caliph.

Muhammad Books of Muhammad He wrote the first manual of arithmetic based on the positional principle. In addition, his treatises on algebra and the calendar have been preserved. Muhammad wrote the famous book "Kitab al-jabr wal-muqabala" "The book of restoration and opposition" (dedicated to the solution of linear and quadratic equations), from the name of which the word "algebra" is derived. A treatise on algebra also includes a chapter on geometry, trigonometric tables, and tables of latitudes and longitudes of cities. He wrote the first manual on arithmetic based on the positional principle. In addition, his treatises on algebra and the calendar have been preserved. Muhammad wrote the famous book "Kitab al-jabr wal-muqabala" "The book of restoration and opposition" (dedicated to the solution of linear and quadratic equations), from the name of which the word "algebra" comes from. A treatise on algebra also includes a chapter on geometry, trigonometric tables, and tables of latitudes and longitudes of cities.

His works Diverse scientific interests of al Khorezmi concerned mathematics, theoretical and practical astronomy, geography and history. Not all of his works have survived. Some of them, mentioned by medieval writers, were subsequently lost. Information about the writings of al-Khwarizmi reported by Eastern historians does not always coincide. It has now been established that al-Khwarizmi was the author of the following works: 1. A book on Indian reckoning; 2. A short book on the calculation of al-jabr and al-muqabala; 3. Astronomical tables; 4. Earth picture book; 5. A book about building an astrolabe; 6. A book about actions with the help of an astrolabe; 7. A book about sundials; 8. Treatise on the definition of the era of the Jews and their holidays; 9. History book.

Algorithm The leadership of al-Khwarizmi played a very important role in the development of arithmetic. The name of the author in the Latinized form Algorismus and Algorithmus began to denote in medieval Europe the whole system of decimal arithmetic. The leadership of al-Khwarizmi played a very important role in the development of arithmetic. The name of the author in the Latinized form Algorismus and Algorithmus began to designate in medieval Europe the entire system of decimal arithmetic.

Al-Khwarizmi also wrote a treatise on Indo-Arabic numerals. The Arabic text has been lost. His Latin translation Algoritmi de numero Indorum and the English counterpart Al-Khwarizmi on the Hindu Art of Calculation gave rise to the mathematical term "algorithm" (from Al-Khwarizmi's name in the title of the book). Al-Khwarizmi also wrote a treatise on Indo-Arabic numerals. The Arabic text has been lost. His Latin translation Algoritmi de numero Indorum and the English counterpart Al-Khwarizmi on the Hindu Art of Calculation gave rise to the mathematical term "algorithm" (from Al-Khwarizmi's name in the title of the book).

Arithmetic "Most easy and useful thing in arithmetic, for example, what a person constantly needs in matters of inheritance, inheritance, division of property, litigation, trade relations or when measuring land, digging canals, geometric calculations, and also in other cases. “The easiest and most useful thing in arithmetic, for example, what a person constantly needs in matters of inheritance, inheritance, division of property, litigation, trade relations or when measuring land, digging canals, geometric calculations, and also in other cases” .

Conceived as an initial guide to practical mathematics, "Al-jabr wal-muqabala" in its first part begins with the consideration of equations of the first and second degree, and then in the two final sections moves on to the practical application of algebra in matters of measurement and inheritance. Conceived as an initial guide to practical mathematics, "Al-jabr wal-muqabala" in its first part begins with the consideration of equations of the first and second degree, and then in the two final sections moves on to the practical application of algebra in matters of measurement and inheritance.

The book begins with an introduction natural numbers, followed by a presentation of the main topic of the first section of the book of solving equations. All presented equations are linear or quadratic and consist of numbers, their squares and roots. It is interesting to note that in all the books of Al-Khwarizmi, mathematical calculations are recorded exclusively with the help of words, not a single symbol, therefore, was used by him. The book begins with an introduction to natural numbers, followed by a presentation of the main theme of the first section of the book of solving equations. All presented equations are linear or quadratic and consist of numbers, their squares and roots. It is interesting to note that in all the books of Al-Khwarizmi, mathematical calculations are recorded exclusively with the help of words, not a single symbol, therefore, was used by him.

A) the squares are equal to the roots; b) squares are equal to numbers; c) roots are equal to numbers; d) squares and roots are equal to numbers, for example, x x = 39; e) squares and numbers are equal to roots, for example, x = 10x; f) roots and numbers are equal to squares, for example, 3x + 4 = x 2. a) squares are equal to roots; b) squares are equal to numbers; c) roots are equal to numbers; d) squares and roots are equal to numbers, for example, x x = 39; e) squares and numbers are equal to roots, for example, x = 10x; f) roots and numbers are equal to squares, for example, 3x + 4 = x 2.

The transformation is carried out through two operations al-jabr and al-muqabala (opposition). Al-Khwarizmi uses the word "al-jabr" in the meaning of "replenishment" to denote the process of transferring negative number from one side of the equation to the other. The transformation is carried out through two operations al-jabr and al-muqabala (opposition). Al-Khwarizmi uses the word "al-jabr" in the meaning of "replenishment" to denote the process of transferring a negative number from one part of the equation to another.

So, using one of the examples of Al-Khwarizmi himself, by means of "al-jabr" the equation x 2 \u003d 40x 4x 2 is reduced to the form 5x 2 \u003d 40x. The term "al-muqabala" means "opposition" and is used by Al-Khwarizmi to refer to the process of reducing equal terms in both sides of the equation. For example, applying the al-muqabala operation twice, we bring the equation x + x 2 = x to the form 21 + x 2 = 7x. So, using one of the examples of Al-Khwarizmi himself, by means of "al-jabr" the equation x 2 \u003d 40x 4x 2 is reduced to the form 5x 2 \u003d 40x. The term "al-muqabala" means "opposition" and is used by Al-Khwarizmi to refer to the process of reducing equal terms in both sides of the equation. For example, applying the al-muqabala operation twice, we bring the equation x + x 2 = x to the form 21 + x 2 = 7x. Example

Further, Al-Khwarizmi shows how to solve six standard types of equations using algebraic methods of solution and geometric proofs. Further, Al-Khwarizmi shows how to solve six standard types of equations using algebraic methods of solution and geometric proofs.

Al-Khwarizmi continues further research in the field of algebra in Hisab al-jabr wal-muqabala, studying how the application of the laws of algebra can be extended to arithmetic solutions of algebraic objects. For example, he shows how to multiply expressions of the form Al-Khwarizmi continues his research in algebra in Hisab al-jabr wal-muqabala, studying how the application of the laws of algebra can be extended to arithmetic solutions of algebraic objects. For example, it shows how expressions like (a + bx) (c + dx) should be multiplied. (a + bx) (c + dx).

Geography And, finally, Al-Khwarizmi was the author of a significant work in the field of geography, where he gave the definition of latitude and longitude 2402 settlements of the world as the basis of the world map. Al-Khwarizmi also wrote a number of other less famous works on topics such as the astrolabe, chronology and sundial. Finally, Al-Khwarizmi was the author of a significant work in the field of geography, where he defined the latitude and longitude of 2402 settlements of the world as the basis of the world map. Al-Khwarizmi also wrote a number of other lesser-known works on topics such as the astrolabe, chronology, and sundials.

MINISTRY OF EDUCATION AND SCIENCE OF THE RB

Bashkir State Pedagogical University

"Al Khorezmi -

outstanding mathematician and astronomer

Ufa - 2004
Content

Introduction ................................................ ............................................... 3

Homeland of al-Khwarizmi ....................................................... ........................... four

Works of al-Khwarizmi ....................................................... ................... 6

Algebra at al-Khwarizmi .............................................. ....................... eight

Conclusion................................................. ...................................... eleven

Literature................................................. ...................................... 12

The full name of al Khorezmi is Abu Adallah (or Abu Jafar) Muhammad ibn Musa al Khorezmi. Translated from Arabic, this means: father of Abdallah (or father of Jafar), Muhammad, son of Musa from Khorezm. Sometimes, in accordance with the Arabic spelling, he is called al Khuwarizmi.

History almost did not preserve biographical information about al Khorezmi. Even the exact dates of his birth and death have not come down to us. It is only known that he was born at the end of the eighth century, and died in the second half of the ninth, more precisely after 847. It is now conventionally accepted to consider the year of his birth 783, and the year of death 850.

In some historical sources al Khorezmi is called “al majusi”, i.e. magician. From this they conclude that his ancestors were magicians - priests of the Zoroastrian religion, widespread in the territory of Central Asia.

Homeland of al Khorezmi

The homeland of the scientist was Khorezm, a vast region of Central Asia, which corresponds to the modern Khorezm region of Uzbekistan, the Tashauz region of Turkmenistan. In historical sources there is no mention of the specific birthplace of al-Khwarizmi, but some indirect considerations allow us to assume that he came from ancient Khiva.

In Khorezm by the beginning of the 9th century. the traditions of an ancient and original culture have developed. We find evidence of this in the writings of medieval Eastern historians. More details about ancient history of this region were obtained thanks to archaeological excavations, which began to be carried out here in Soviet times. Valuable finds of archaeologists, supplementing the reports of medieval writers, made it possible to get an idea of the highly developed civilization of ancient Khorezm.

The remains of a grandiose irrigation system have been discovered on the territory of Khorezm. It was created long before the beginning of our chronology - in the II millennium BC. e. The developed irrigation economy of Khorezm determined high level the entire economy of the region. In ancient books there are reports of large, well-fortified cities of Khorezm. For example, the Fir castle, built on the banks of the Amu Darya at the beginning of the 4th century, was surrounded by three rows of high walls and was visible at a distance of about twenty kilometers.

During the excavations, magnificent works of Khorezm artists and sculptors were found. Khorezmian merchants carried on a lively trade with India and China, the Middle East, the Caucasus and Eastern Europe. They exported furs, cattle, fish.

Already in very distant times, the Khorezmians owned a written language. Monuments of this writing were discovered during archaeological excavations and deciphered by scientists. Already in ancient times, the foundations of exact sciences were formed in Khorezm. The achievements of the Khorezmians in the field of economic life would have been impossible without certain knowledge in mathematics, geodesy, astronomy, etc.

For example, the construction of canals, fortresses, multi-storey palaces required not only practical skills, but also the ability to accurately level the terrain and perform complex calculations and measurements. Traveling to distant countries through deserts would be impossible without the ability to navigate by the stars, that is, without mastering the rudiments of astronomy.

Founded in the 60s. 8th century the city of Baghdad became new capital Arab Caliphate. Baghdad quickly became an important center for trade, science and culture. The city, where people came from various regions of the caliphate, was crowded and lively, famous for its bazaars.

A large scientific school arose in Baghdad, which attracted outstanding scientists from different countries. A library was created, replenished with valuable scientific works. The "House of Wisdom" was founded - an institution that performed the functions of the Academy of Sciences. At the “House of Wisdom” there was a rich library of old manuscripts and an astronomical observatory. Al Khorezmi was also recruited to work in the “House of Wisdom”.

Al Khorezmi's writings

Diverse scientific interests of al Khorezmi concerned mathematics, theoretical and practical astronomy, geography and history. Not all of his works have survived. Some of them, mentioned by medieval writers, were subsequently lost.

Information about the writings of al-Khwarizmi reported by Eastern historians does not always coincide. It has now been established that al-Khwarizmi was the author of the following works:

1. "The book of the Indian account";

2. “A short book on the calculation of al-jabr and al-muqabala”;

3. "Astronomical tables";

4. “The book of the picture of the Earth”;

5. “The book on the construction of an astrolabe”;

6. “A book about actions with the help of an astrolabe”;

7. “The Book of Sundial”;

8. "Treatise on the definition of the era of the Jews and their holidays";

9. "The Book of History".

Of these works, only seven have come down to us - in texts belonging either to al-Khwarizmi himself or to his medieval commentators.

The geographical treatise “The Book of the Picture of the Earth” is the first known work on geography in Arabic. He had a strong influence on the further development of this science in the countries of the East.

Al Khorezmi paid great attention to astronomy. His main task in this area is the compilation of zij, i.e. astronomical and trigonometric tables necessary for solving problems of theoretical and practical astronomy. In this work, for the first time in literature in Arabic, a table of sines was given and a tangent was introduced. Zij al Khorezmi was very popular not only in the East, but also in Europe. The leading Eastern astronomers did not refer to him. At the beginning of the XII century. it was translated into Latin and became available to European scholars after that. In addition to the zij, al Khorezmi described the calendar systems of different peoples.

Al Khorezmi has made important contributions to the development of practical astronomy. He wrote a treatise on the design and use of the astrolabe, the main instrument that served in the Middle Ages to observe the starry sky.

The “Book of History” or the “Book of the chronology” is mentioned in several medieval writings. Therefore, al-Khwarizmi is ranked among the earliest historians who wrote in Arabic.

The greatest fame in the history of science of al-Khwarizmi was brought by his mathematical works.

Algebra at al-Khwarizmi

The algebraic treatise of al-Khwarizmi is known under the title: “A Brief Book of Complementation and Contradiction” (in Arabic: “Kitab mukhtasar al-jabr wal-muqabala”). The treatise consists of two parts - theoretical and practical. The first of them presents the theory of linear and quadratic equations, and also touches upon some questions of geometry. In the second part, algebraic methods are applied to solving specific household, commercial and legal problems.

In the introduction, al-Khwarizmi talks about what prompted him to take up writing the essay: “I compiled short book about the calculation of algebra and almuqabala, which contains simple and complex questions of arithmetic, because this is necessary for people when dividing an inheritance, drawing up wills, dividing property and court cases, in trade and all kinds of transactions, as well as in the measurement of land, the construction of channels, geometry and other varieties of such cases. Thus, it is emphasized that various applied problems can be solved with the help of algebraic methods.

Further, al-Khwarizmi shows which numbers are used in algebra. If arithmetic operates with ordinary numbers, which are “made up of units”, then numbers appear in algebra special kind- an unknown quantity, its square and a free term of the equation.

Al Khorezmi calls the unknown value the term “root” (djizr) and gives the following definition: “A root is any thing that is multiplied by itself, whether it is a number equal to or greater than one, or a fraction less than it.” This definition is due to the fact that when solving equations, they always looked for not only x, but also x 2. Therefore, the unknown was considered as the square root of the unknown. The definition also emphasizes that the unknown can take both integer and fractional values. The term “root” used by al-Khorezmi is, in all probability, a translation of the Sanskrit word “mula” (“root of a plant”), which Indian mathematicians denoted an unknown in an equation. Later, in Arabic literature, the term “thing” (“shay”) was used for the same purpose.

The square of the unknown is called the word “property” (“small”) and is defined as “what is obtained from the root when it is multiplied by itself”.

The free term of the equation - "prime number" - al-Khwarizmi calls "dirhem", i.e. monetary unit.

Then he proceeds to the classification of linear and quadratic equations. At present, it seems to be completely redundant, since all special cases are combined using the notation ax 2 +bx+c=0, where the coefficients a, b and c can take positive, negative and zero values. But in the time of al-Khwarizmi, the situation was different: there was not only a letter designation, but also the concept of a negative number. Therefore, the equation only made sense if all of its coefficients were positive.

Al Khorezmi distinguishes the following six types of equations:

1. “squares are equal to roots”, which in modern notation means ax 2 = bx;

2. “squares are equal to a number”, i.e. ax 2 =c;

3. “the roots are equal to the number”, i.e. ax=c;

4. “squares and roots are equal to a number”, i.e. ax 2 +bx=c;

5. “squares and numbers are equal to roots”, i.e. ax 2 +c=bx;

6. “the roots and numbers are equal to the square”, i.e. bx+c=ax 2 .

Examples are given for each of these types.

In order to reduce this equation to one of the specified types, al-Khwarizmi introduces two special actions. The first is al-jabr, which means replenishment. It consists in transferring the negative term from one side of the equation to the other. From this term arose modern word"algebra".

The second act is al-muqabala, which means opposition. It consists in canceling equal terms on both sides of the equation.

In addition, it was required that the coefficient at the highest term be equal to one. Later, in some works of Eastern scientists, even special algebraic operations appeared - “additions” (al-takmil) and “reduction” (ar-rad). The first of these consisted in multiplying all terms of the equation by the reciprocal of the coefficient a in the equation ax 2 +bx+c=d if a>1. The second meant a similar operation if a<1. Встречался также специальный термин (аль-хатт), обозначающий действие деления коэффициентов уравнения на общий множитель.

Al Khorezmi considers various tasks about the division of the inheritance. For example: “A man died leaving two sons and bequeathed a third of his property to another man. He left 10 dirhams in cash and a loan equal to the share of one of them.”

Following al-Khwarizmi's reasoning, let's denote the debt by x. Then all the property is equal to 10+x. since the three heirs receive equal shares, then (10+x)/3=x, whence x=5.

The algebraic methods of al-Khwarizmi were also used in the chapter on geometry.

Conclusion

Mohammed ibn Musa al Khorezmi occupies an important place among the scientists of Central Asia, whose names entered the history of exact natural science. In the ninth century - at the dawn of the dawn of medieval oriental science - the scientist made a great contribution to the development of arithmetic and algebra. Algebraic treatise al-Khwarizmi was among the first works on mathematics translated in Europe from Arabic into Latin. in Europe until the 16th century. algebra was called "the art of algebra and almuqabala". The modern name algebra comes from the word al-jabr. And on behalf of al Khorezmi, the word algorithm came about.

Al Khorezmi gives rules for calculating the area of a square, triangle and rhombus. Gives the rules for calculating the volume, including the truncated square pyramid. He compiled calendars, wrote about chronology. His merits in astronomy are great, although, like his astronomers contemporaries, he proceeded from the geocentric system of the world. He made a great contribution to mathematical geography. Al Khorezmi for the first time in Arabic described in detail the then known inhabited part of the Earth, gave its map indicating the coordinates of the most important settlements, depicting seas, islands, mountains, rivers, etc.

The works of al-Khwarizmi had a strong influence on scientists of East and West for several centuries and served as a model for writing mathematics textbooks for a long time.

Literature

1. S. Kh. Sirazhetdinov, G. P. Matvievskaya. Al Khorezmi is an outstanding mathematician and astronomer of the Middle Ages. M.: Enlightenment, 1983.

2. Yushkevich A. P. History of mathematics in the Middle Ages. Moscow: Fizmatgiz, 1961.

Full name - Abu Abdallah (or Abu Jafar) Muhammad ibn Musa al-Khwarizmi. Translated from Arabic, this means: father of Abdallah (or father of Jafar), Muhammad, son of Musa from Khorezm. Sometimes - in accordance with the Arabic spelling - he is called al-Khuvarizmi.

History almost did not preserve biographical information about al-Khwarizmi. Even the exact dates of his birth and death have not come down to us. It is only known that he was born at the end of the eighth century, and died in the second half of the ninth, more precisely after 847. Now it is conventionally considered to be the year of his birth in 783, and the year of death in 850.

In some historical sources, al-Khwarizmi is called "al-majusi", i.e. magician. From this they conclude that his ancestors were magicians - priests of the Zoroastrian religion, widespread in the territory of Central Asia.

Al-Khwarizmi belonged to those Central Asian scientists who were recruited to work in the capital of the Arab Caliphate, Baghdad. There were many such scientists. Among the contemporaries of al-Khwarizmi, who lived in Baghdad, one can name, for example, the famous astronomers Abu-l-Abbas Ahmad al-Fargani and Ahmad ibn Abdallah al-Marvazi, known as Khabash al-Khasib. The first of them came from Fergana, the other - from Merv.

At that time, special attention was paid to the achievements of ancient Greek and Hellenistic science. The works of the classics of antiquity were collected and translated into Arabic. However, Baghdad scholars of the 8th - 9th centuries. were not only translators and commentators. They also engaged in independent research and achieved remarkable results in various fields of knowledge.

Science in Baghdad reached its greatest flourishing under the son of Harun al-Rashid, Caliph al-Mamun, who ruled from 813 to 833. Under him, the "House of Wisdom" (bayt al-hikma) was founded - an institution that performed the functions of the Academy of Sciences. Famous historian of the X century. An-Nadim reports that Muhammad ibn Musa, a native of Khorezm, was attracted to the "House of Wisdom" of Caliph al-Mamun.

Until 813, al-Mamun was the governor of the eastern provinces and lived in Merv. It is possible that here he met with al-Khwarizmi, and subsequently invited him to Baghdad.

In one of his works, al-Khwarizmi praised al-Mamun. He noted his "love for science and the desire to bring scientists closer to him, extending the wing of his patronage over them and helping them in clarifying what is unclear to them, and in alleviating what is difficult for them" .

There is no doubt that the scientists who worked at the "House of Wisdom" made a huge contribution to mathematics, astronomy and other sciences. They carried out, for example, measuring the length of a degree of the meridian in order to clarify the value of the circumference of the Earth, found in antiquity. An arc value of 1° was found, close to the true value ("111 km"). Historians believe that al-Khwarizmi also took part in this work.

Detailed information about the Baghdad period of his life has not been preserved either. There are reports that he made two trips: one to the country of the Khazars, and the other to Byzantium. However, it is difficult to say that this information is reliable.

The latest date associated with the name of al-Khorezmi is 847. Caliph al-Vasik died this year, and al-Khorezmi is mentioned among those present at his death.

Thus, we see that very few facts from the life of the great Central Asian scientist have been preserved. Therefore, historians of science should base themselves mainly on the study of his writings. Diverse scientific interests of al-Khwarizmi concerned mathematics, theoretical and practical astronomy, geography and history. Not all works written by al-Khwarizmi have been preserved. Some of them, mentioned by medieval writers, were subsequently lost.

The geographical treatise of al-Khwarizmi "The Book of the Picture of the Earth" is the first known work on geography in Arabic. He had a strong influence on the further development of this science in the countries of the East.

Al-Khwarizmi (full name - Abu Abdullah Muhammad ibn Musa al-Khwarizmi) - mathematician, astronomer and geographer of the 9th century. The name of Al-Khwarizmi indicates his homeland - the state of Khorezm, and one of the nicknames of the scientist - Al-Majusi - speaks of his origin from the Zoroastrian priests - magicians (in Arabic "majus").

The full name of al-Khwarizmi is Abu Abdallah (or Abu Jafar) Muhammad ibn Musa al-Khwarizmi. Translated from Arabic, this means: father of Abdallah (or father of Jafar), Muhammad, son of Musa from Khorezm. Sometimes - in accordance with the Arabic spelling - he is called Al-Khuvarizmi.

History almost did not preserve biographical information about Al-Khwarizmi. Even the exact dates of his birth and death have not come down to us. It is only known that he was born at the end of the eighth century, and died in the second half of the ninth, more precisely after 847. Now it is conventionally considered to be the year of his birth in 783, and the year of death in 850.

In some historical sources, Al-Khwarizmi is called "Al-Majusi", i.e. magician. From this they conclude that his ancestors were magicians - priests of the Zoroastrian religion, widespread in the territory of Central Asia.

Al-Khwarizmi belonged to those Central Asian scientists who were attracted to work in the capital of the Arab caliphate, Baghdad. There were many such scientists. Among the contemporaries of al-Khwarizmi, who lived in Baghdad, one can name, for example, the famous astronomers Abu-al-Abbas Ahmad Al-Fargani and Ahmad ibn Abdallah Al-Marvazi, known as Khabash Al-Khasib. The first of them came from Fergana, the other - from Merv.

Baghdad was founded in the 60s. 8th century caliph Al-Mansur from the Abbasid dynasty, who ruled from 754 to 775. The new capital of the state, which at that time occupied a vast territory, quickly became an important center of trade, science and culture.

Governing a huge state was not easy. The rulers of the caliphate realized that their economic and military plans could not be realized if the knowledge that the conquered peoples owned was not mastered. Therefore, the rulers contributed in every possible way to the development of science. A large scientific school arose in Baghdad, which attracted outstanding scientists from different countries. A library was created, replenished with valuable scientific works.

Particular attention at this time was shown to the achievements of ancient Greek and Hellenistic science. The works of the classics of antiquity were collected and translated into Arabic. Special expeditions were equipped to buy manuscripts.

Of particular interest were the exact sciences - mathematics, astronomy, geodesy, mathematical geography. The "Beginnings" of Euclid, the "Almagest" of Ptolemy, the "Sphere" of Menelaus and others were translated. Indian astronomical writings were also studied. However, Baghdad scientists of the VIII - IX centuries. were not only translators and commentators. They also engaged in independent research and achieved remarkable results in various fields of knowledge.

The successors of Caliph Al-Mansur continued to patronize science. His grandson Harun Ar-Rashid, who ruled from 786 to 809, is known (albeit in a very idealized form) from the tales of the Thousand and One Nights. Science in Baghdad reached its greatest flourishing under the son of Harun Ar-Rashid, Caliph Al-Mamun, who ruled from 813 to 833. Under him, the “House of Wisdom” (bayt al-hikma) was founded, an institution that performed the functions of the Academy of Sciences. At the “House of Wisdom” there was a rich library of old manuscripts and an astronomical observatory.

In Baghdad, among other scientists of this academy, Al-Khwarizmi worked for many years. Famous historian of the X century. An-Nadim reports that Muhammad ibn Musa, a native of Khorezm, was attracted to the "House of Wisdom" of Caliph Al-Mamun.

Until 813, Al-Mamun was the governor of the eastern provinces and lived in Merv. It is possible that here he met with Al-Khwarizmi, and subsequently invited him to Baghdad.

In one of his works, Al-Khwarizmi praised Al-Mamun. He noted it: "love for science and the desire to bring scientists closer to him, stretching over them the wing of his patronage and helping them in clarifying what is unclear to them, and in alleviating what is difficult for them."

It is not known how active Al-Mamun's personal participation in scientific work was in reality, but there is no doubt that the scientists who worked at the "House of Wisdom" made a huge contribution to mathematics, astronomy and other sciences. They carried out, for example, measuring the length of a degree of the meridian in order to clarify the value of the circumference of the Earth, found in antiquity. An arc value of 1° was found close to the true value (111 km). Historians believe that Al-Khwarizmi also took part in this work.

The latest date associated with the name of Al-Khorezmi is 847. Caliph Al-Vasik died this year, and Al-Khorezmi is mentioned among those present at his death.

Thus, we see that very few facts from the life of the great Central Asian scientist have been preserved. Therefore, historians of science should base themselves mainly on the study of his writings. Diverse scientific interests of Al-Khwarizmi concerned mathematics, theoretical and practical astronomy, geography and history. Not all works written by Al-Khwarizmi have been preserved. Some of them, mentioned by medieval writers, were subsequently lost.

He wrote the first manual on arithmetic based on the positional principle. In addition, his treatises on algebra and the calendar have been preserved. Muhammad wrote the famous book "Kitab al-jabr wal-muqabala" - "The Book of Restoration and Opposition" (dedicated to the solution of linear and quadratic equations), from the name of which the word "algebra" comes from. A treatise on algebra also includes a chapter on geometry, trigonometric tables, and tables of latitudes and longitudes of cities.

The leadership of al-Khwarizmi played a very important role in the development of arithmetic. The name of the author in the Latinized form Algorismus and Algorithmus began to designate in medieval Europe the entire system of decimal arithmetic. Subsequently, the word "algorithm" began to denote any regular process that, in a finite number of steps, gives a solution to a certain class of problems.

The geographical treatise of Al-Khwarizmi "The Book of the Picture of the Earth" is the first known work on geography in Arabic. He had a strong influence on the further development of this science in the countries of the East.

Abu Ab-dal-lah Mu-ham-mad ibn Mu-sa al-Kho-rez-mi / 783 - 850 / - one of the largest scientists of the Middle Ages. His ro-di-na is Kho-resm. Your knowledge of al-Kho-rez-mi so-vershenst-vo-val in “Do-me mud-ros-ty” in Bagh-da-de. This was a school-dir-de-nie was of its own kind Aka-de-mi-ey na-uk, in a swarm of ra-bo-ta-whether many scholars are Arab th Vos-th-ka. "House of Mud-ros-ti" was famous for its god-ha-that bib-lio-te-koy old ru-ko-pi-sey and ast-ro-no-mi-ches -koy about-ser-va-to-ri-her.

Is-sle-to-va-te-whether mouth-no-vi-li that al-Kho-rez-mi was the author of 9 co-chi-non-ny:

A book about Indian arith-me-ti-ke;

A short book about the is-number-le-nii of al-geb-ry and al-mu-ka-ba-ly;

Ast-ro-no-mi-chess tables (zij);

Books of kar-ti-ny of the Earth;

Books about the building-e-nii ast-ro-la-bii;

A book about action-vi-yah with the help of ast-ro-la-bee;

Books about solar hours;

Trak-tat about the opre-de-le-nii of the era of ev-re-ev and their holidays;

Book of is-it-rii.

So-chi-non-nie al-Ho-rez-mi about arif-me-ti-ke syg-ra-lo the most important role in the history of ma-te-ma-ti-ki and ho -tya his Arabic original text lost-ryan, co-der-zha-nie from the West, but according to the Latin translation of the 12th century. In this co-chi-not-nii for the first time, yes, but sis-te-ma-ti-ches-something from-lo-same-arif-me-ti-ki, os-no-van-noy on de -sya-tych-noy in-zi-qi-on-noy sys-te-me numeration.

Al-geb-ra-i-ches-kaya book-ga al-Kho-rez-mi (Ki-tab mukh-ta-sab al-jabr and wa-l-mu-ka-ba-la) co-sto- it from two parts - te-o-re-ti-ches-koy (the-o-riya re-she-linear and square equations, not-to- then-rye questions of geo-metries) and practical-ti-ches-coy (with-me-not-nie al-geb-ra-i-ches-methods in re-she -nii of economics-veins-but-be-that-outs, tor-go-outs and yuri-di-chess-tasks - de-lying on-consequence-va, compiling-le-tion for -ve-shcha-ny, division of imu-shchest-va, various personal transactions, from me-re-land, construction of canals). Thankfully, the Arabic word “al-jabr” arose such a scientific term as “al-geb-ra”. Unas-le-to-van-noe from the east ma-te-ma-ti-kov the doctrine of linear and square equations-no-no-yah became os -new development of al-geb-ry in Europe. La-ti-ni-zi-ro-van-noe name of the scholar-no-go entered science under the term "al-go-rhythm".

Geo-met-ri-ches-kaya part of the trak-ta-ta in a sacred way from me-re-tion of the area and volumes of geo-met-ri-ches-kih fi-gur (triangle-nick, square, rhombus, para-ral-le-lo-gram, circle, circle segment, four-you-reh-coal-nick with different hundred-ro -na-mi and corner-la-mi, pa-ral-le-le-pi-ped, kru-go-howl chi-lin-dr, pris-ma, co-nus).

Og-ro-men, the contribution of the scientist-no-go and to ast-ro-no-miya, someone-paradise would-la not-ob-ho-di-ma for oro-sha-e-mo-go earth- le de lia, sea and su-ho-put-noy tor-gov-whether. Zij (collection-nickname ast-ro-no-mi-ches-kih and three-go-no-met-ri-ches-kih tables) al-Ho-rez-mi in-sacred chrono-no- lo-gyi and ka-len-da-ryu (important on-learning on-right-le-tion, since different people used poly-zo-wa-lis different personal -mi sis-te-ma-mi time-men-no-th account). Of great importance for the astra-ro-no-mii of that time was the presentation of his book about astra-ro-la-bee.

Al-Kho-rez-mi also made a significant contribution to geo-graphics. He considers the author of the first co-chi-non-niya according to ma-te-ma-ti-chess geo-graphics. For the first time, in Arabic, he described the known by that time obi-that-e-mu part of the Earth, gave a map with ko-or-di -on-ta-mi of the most important on-the-se-len-th points, with sea-mi and ocean-a-na-mi, mountains-ra-mi and re-ka-mi. What does it have to do with it Book-ga car-ti-ny Earth-li- not just a re-re-water co-chi-not-ni pre-pole-vein-ni-kov, but an original work containing a lot of new data. He or-ga-ni-zo-val on-scientific ex-pe-di-tions in Vi-zan-tiya, Kha-za-riyu, Af-ga-nis-tan. Under his leadership, you would-la-number-le-for the length of one-and-th city-du-sa earth-no-go me-ri-di-a-na.

Despite his raz-nose-that-ron-ny circle on-scientific in-te-re-owls, the main science of his life is ma-te-ma-ti-ka . al-Kho-rez-mi for the first time presented al-geb-ru as a science of general methods for resolving chi-s-lo-linear and square equations, gave the class-si-fi-ka-tion of these equations.

From the famous is-to-rik na-uki J. Sar-ton called him “we-li-chai-shim ma-te-ma-ti-com of his-e-th time-me-ni and , if you take into account all the things about me, one of the greatest of all times.

By ma-te-ri-a-lam: Si-razh-di-nov S., Mat-vi-ev-skaya G. Al-Kho-rez-mi - you-da-y-u-schy-sya ma-te-ma-tik and ast-ro-nome environments -not-ve-kovya. M., "Pro-sve-shche-nie", 1983