Brief historical information about the appearance of the shot. History of the vinification of primary fractions. Traditional methodical approaches to the development of "Significant fractions"
Slide 2
Vikonala: 5th grade student Svitlana Kuznetsova Kerivnik: Kukushkina N.G. teacher of mathematics
Slide 3
Wine of shotguns. Fractions in Ancient Egypt. Fractions in Ancient Babylon. Fractions in Ancient Rome. Fractions in Ancient Greece. Fractions in Russia. Fractions in Ancient China. Fractions in other ancient and middle powers. Conclusion References
Slide 4
Enter
Why did we begin to twist simple fractions? Even non-numerical numbers, starting with their non-numerical notation and ending with complicated rules for dealing with them. Although from the first acquaintance with them it became clear that without them we cannot manage in basic life, so that every day we have to fall into pieces with the whole problem, and I have a feeling that we cannot be left whole i, and dribnі. numbers.
Slide 5
Behind them, the light appeared folded, but suddenly dwindled. I have a lot of food. What fractions are needed? Why are stinks important? I wanted to know, the stars came to us fractions, who figured out the rules of working with them. If you want to come up with a word, perhaps it’s not even possible, since everything in mathematics has been verified, since all the sciences and developments in our life revolve around clear mathematical laws that exist throughout the world. It cannot be that in our country the addition of fractions follows one rule, but in England it is different.
Slide 6
Wine of fractions
The Russian term “fraction”, like its analogues in other languages, is similar to the Latvian one. fractura, which, in its own way, is a translation of the Arabic term with the same meanings: lamati, to fragment. Therefore, perhaps, the first fractions through the boules are fractions in the form of 1/n. Further development naturally follows from considering these fractions as units, from which fractions m/n can be added - rational numbers. However, this path was not realized by all civilizations: for example, it was never realized in ancient Egyptian mathematics.
Slide 7
The first fraction, which people knew, was half. Although the names of all the advancing fractions are connected with the names of their signifiers (three – “thirds”, even – “quarter”, etc.), for half it is not so - their names in all languages do not have anything similar to the word “two”.
Slide 8
Fractions in Ancient Egypt
In Ancient Egypt they used only the simplest fractions, which have ancient units (what we call “fractions”). Mathematicians call such fractions aliquots (from the Latin aliquot – splinter). The names of main fractions and single fractions are also discussed.
Slide 9
The Egyptians used only two fractions and in parts - two thirds and three quarters. These fractions were often condensed in calculations. Special symbols were created for them, a special sign for the fraction 1/2.
Slide 10
Nina sum of many aliquot shot is called Egyptian shot. In other words, the sum of the number is the number, the equal number, and the sign, which is a natural number.
Slide 11
One of the first known riddles about Egyptian fractions is Rinda's Mathematical Papyrus. Three older texts in which Egyptian fractions can be guessed are the Egyptian Mathematical Book of Suviy, the Moscow Mathematical Papyrus and the Wooden Tablet of Akhmim. The most recent monument of Egyptian mathematics, also known as the "Moscow Papyrus", is a document from the 19th century BC. It was founded in 1893 to collect the ancient treasures of Golenishchev, and in 1912 it passed into the hands of the Moscow Museum of Exquisite Mysteries. He had 25 different orders.
Slide 12
Fractions in Ancient Babylon
It appears that the ancient Babylonians used the sixty number system. This fact is connected with the fact that the Babylonian penny and one hundred coins of the world were divided from historical minds into 60 equal parts: 1 talent = 60 times; 1 mina = 60 shekels. Sixty parts were central to the life of the Babylonians. The very same stinks were painted with sixty fractions, waving the banner of the first number 60 of the 5th level: 602 = 3600, 603 = 216000 then. These are systematic fractions, then. fractions whose standard is the degree of that same number.
Slide 13
Following the Babylonian sixtieth system of numbers, they were used in modern science at the time of extinction and culture. To this day there have been preserved divisions of Godini for 60 khvilin, khvilin for 60 seconds, cola for 360 degrees, degrees for 60 khvilin, khvilin for 60 seconds Khvilina means in Latin “small part”, second is “friend”
Slide 14
Fractions in Ancient Rome
The Romans used only concrete fractions, which replaced abstract parts with subdivisions of vicoristic approaches. This system of shotguns was divided into 12 parts of one shot, which was called ass. This is how Roman decimal fractions appeared, then. There are already twelve of them who have a banner. The twelfth part of an ass was called an ounce. Instead of 1 \ 12 the Romans said “one ounce”, 5 \ 12 - “five ounces”, etc. Three ounces were called a quarter, four ounces - a third, six ounces - a half.
Slide 15
In order to work with such fractions, it was necessary to memorize a table and a multiplication table for these fractions. Therefore, the Roman merchants knew for sure that with the addition of a trienza (1/3 asses) and a sextance, it would yield seven, and with the multiplication of a demon (2/3 asses), a sessunction (2/3 ounce, that is, 1/8 asses) would yield an ounce. To make the work easier, special tables were created, and some of them have come down to us.
Slide 16
Fractions in Ancient Greece
In Ancient Greece, arithmetic - the concept of the hidden power of numbers - was reinforced in the form of logistics - the mysticism of calculation. The Greeks appreciated that fractions could be used in logistics. The Greeks freely operated all arithmetic operations with fractions, but recognized them with numbers. There were no fractions lost in the Greek works of mathematics. The Greeks always respected the fact that mathematics can deal with only whole numbers. Merchants, craftsmen, as well as astronomers, surveyors, mechanics and other “black people” were given the opportunity to deal with stink shot. “If you want to share one, mathematicians will mock you and not allow you to work,” wrote the founder of the Athens Academy, Plato.
Slide 17
The fragments of the Greeks worked in small fractions more sporadically; Heron and Diophantus wrote fractions in alphabetical form, with the number sign below the sign sign. For some fractions, the boundaries of the symbols were fixed, for example, for 12 - L′, but in general their alphabetical numbering forcibly allowed fractions to be designated.
Slide 18
Fractions in Russia
The first Russian mathematician, known to us in his name, the monk of the Novgorod monastery Kirik, was engaged in the study of chronology and calendar. His handwritten book “It is important for people to know the number of all fates” (1136 rubles), then. “Revolution, how people know the summer” is divided into five years, twenty five, etc. parts, as he called them “the ancient year” or “pieces of hours”. To reach the seventh shotgun, which is 937,500 in the day and night, and it seems as if nothing will come of the same shotgun.
Slide 19
In the cob shape of the planks, the shells are specially attached to the needs of advanced arithmetic. This system of taxation in Russia in the 15th-17th century, when it was necessary to carry out the operations themselves with fractions, as a result of the mental unit nya - plow, divided into parts.
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Fractions in Ancient China
In China, all arithmetic operations with elementary fractions were already established before the II century. to sound e.; It is described in the fundamental body of mathematical knowledge of ancient China - “Mathematics in Nine Books”, the remaining edition of which belongs to Zhang Tsang. Calculating on the basis of a rule similar to Euclid’s algorithm (the greatest number of numbers and numbers), Chinese mathematicians shortened fractions. The multiplicity of fractions was revealed as the location of the area of a rectangular plot of land, the width of which is expressed by fractional numbers. The division looked at another idea of the division, in which the Chinese mathematicians did not care that the number of participants in the division could be shot, for example, 3⅓ people.
Slide 21
The division of shot in Jiuzhangsuanshu is different from what is accepted today. The rule “jingfen” (“order of division”) states that before dividing the fractions, they must be brought to the final sign. Thus, the procedure for dividing the fractions has the following stage: a/b: c/d = ad/bd: cb/bd = ad/cb. Lische at V Art. ZhangQiu-jian, in his work “ZhangQiu-jiansuanjing” (“The Rhunkov Canon of ZhangQiu-jian”), recalled this and vibratedly divided the fractions according to the primary rule: a/b: c/d = ad/cb.
Slide 22
Visnovok
I have learned that the history of small fractions is a winding road with many obstacles and difficulties. While working on the abstract, I learned a lot of new things. I read a lot of books and sections of the encyclopedia. I got to know the first fractions that people used, the concepts of aliquot fractions, I learned new names for people who made their contribution to the development of knowledge about fractions.
Slide 23
List of references
1.Borodin A.I. On the history of arithmetic. Golovne vidavnitstvo "Vishcha school" - K., 1986 2. Glazer G. I. History of mathematics in school: IV-VI grades. Handbook for readers. - M.: Prosvitnitstvo, 1981. 3. Ignatiev E.I. The kingdom is gentle. Head editorial office of physical and mathematical literature of the publishing house “Science”, M., 1978. 4. Kordemsky G.A. Mathematical complexity.-10th type, revised. І additional-M.: Unisam, MDS, 1994. 5. Stroik D.Ya. A short sketch of the history of mathematics. M.: Nauka, 1990. 6. Encyclopedia for children. 11. Mathematics. Moscow, "Avanta +", 1998. 7. http://ua.wikipedia.org/wiki.Material from Wikipedia - the free encyclopedia.
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The first fraction, which people knew, was half. Let's step on the tretina. Both the Egyptians and the Babylonians had special meanings for fractions 1/3 and 2/3, but did not follow the meanings for other fractions.
The Egyptians tried to write down all fractions as sums of fractions, so that fractions look like 1/n. For example, instead of 8/15 they wrote 1/3+1/5. Let's face it, as we said, 2/3. Sometimes it was done manually. Papyrus Ahmes has a mission:
"Divide 7 loaves of bread among 8 people."
If you cut leather bread into 8 pieces, you will have to make 49 cuts.
And in Egyptian the story went like this. The fraction 7/8 was written in the following form: 1/2 + 1/4 + 1/8. Well, every human being needs a portion of bread, a quarter of bread, and an eighth of bread; Therefore, the bread is cut in bulk, two loaves - into 4 pieces and one bread - into 8 pieces, after which each piece is given to each person.
It would have been impossible to put together such fractions by hand. Even both additions can include the same parts, and then, when added, they appear as 2/n. But the Egyptians did not allow such shots. Therefore, the Ahmes papyrus begins with a table, where all fractions of this type from 2/5 to 2/99 are written in the form of sums. Following this table, a subset of numbers was added. The axis, for example, is 5 divided by 21:
The Egyptians also multiplied and divided fractions. To multiply, I had to multiply the parts by parts, and then, perhaps, I’ll recreate the table. It was even more folding on the right side of the split. The Babylonians followed a completely different path. The stinks worked with more than sixty fractions. Some symbols of such fractions are the numbers 60, 60 2, 60 3, etc., such fractions as 1/7 could not be accurately expressed through sixties: they were determined approximately. Since then, the numerical system of the Babylonians was positional; they used sixtieth fractions using the same table as for natural numbers.
Greek and Arabic mathematicians and astronomers used sixty fractions that fell to Babylon. It was difficult to work with natural numbers written in the tens system and fractions written in the sixties system. And it was even more important to work with small fractions. Therefore, the Dutch mathematician Simon Stevin urged to move to tens of fractions. From the very beginning they wrote very smoothly, but then they gradually moved on to the current recording. At the same time, EOM uses two fractions, as they were used in Russia: half, quarter, half, half, etc.
The Tsikava shot system was in Ancient Rome. Vaughn was grounded on a division into 12 parts of one vaga, which was called ass. The twelfth part of an ass was called an ounce. And along the way, sometimes other magnitudes matched the night river - the wagon. For example, the Roman could say that he had passed this ounce of a book, or had read five ounces of a book. In this case, obviously, there was no mention of the name of the nobleman or the book. I am glad that 7/12 of the route has been completed or 5/12 of the book has been read.
And for fractions that come out as shortened fractions with the sign 12 or fragmentation of twelve parts into fractions, there were special names. They sometimes say: “He has scrupulously applied his food.” This means that the nutrition has been completed to the end, so that the least amount of ambiguity is not lost. And the wonderful word “scrupulous” appears from the Roman name for 1/288 asses - “scrupulus”. The following names are used: “semis” - half an ass, “sextans” - half a part, “semіuncіya” - half, then 1/24 ass, etc. Usyogo has 18 different names of fractions. To work with fractions, you need to store several fractions, an addition table, and a multiplication table. Therefore, the Roman merchants knew for sure that from the folded triens (1/3 asses) and sextance it would cost sevens, and when multiplied by a demon (2/3 asses) to a sessunction (3/2 ounce, then 1/8 assa) it would yield an ounce. To make the work easier, special tables were created, and their actions have come down to us.
Through those in the twelve system there are a lot of fractions with the signifiers 10 or 100, the Romans could not divide by 10, 100 or even. d. Ale from the surplus of wine without having to worry about it. In order not to cope with such calculations, the Romans began to vicorize hundreds. They took too much from the borrower (it was just pennies on top of what was given to the borrower). In front of this they said: not “you will pay a surplus of 16 hundred sumi to the Borg,” but “for every 100 sisters of the Borg you will pay 16 sisters of a surplus.” And it was said the same, and there were no shots fired! Since the words “per hundred” sounded like the Latin “pro centum,” the hundredth part began to be called the hundred part. And now we want fractions, and especially tens of fractions, as everyone knows, hundreds of fractions will still be found in financial affairs, and in planning, and in various aspects of human activity. And before, they used to stove even more milles - that’s what parts of a thousand were called (in Latin “about miles” - per thousand). In addition, in the form of hundreds, they are indicated by the % sign, and promils are indicated by the % o.
There were no fractions lost in the Greek works of mathematics. The Greeks always respected the fact that mathematics can deal with only whole numbers. Merchants, craftsmen, as well as astronomers, surveyors, mechanics and other “black people” were given the opportunity to get involved with stink shot. It’s always been common to say: “Drive nature at the door - it’ll fly in at the window.” That’s why fractions penetrated into the strictly scientific works of the Greeks “from the back door.” Besides arithmetic and geometry, music was included before Greek science. The Greeks called music the meaning of harmony. The price spiraled down to that part of our arithmetic that deals with centimeters and proportions. The Greeks knew: when a long string is stretched, the lower sound comes out, and the short string produces a high sound. But any musical instrument has not one, but many strings. In order for all the strings to sound “harmonious” when playing, acceptable to the ear, the majority of the parts that sound are their responsibility as a singer. That is why the concept of notes and fractions was discussed in the Greek theory of music.
A modern system for recording fractions using numbers and numbers was created in India. Only the people there wrote the sign of the fire, and the number - below and wrote shot rice. And the Arabs began to write down fractions accurately.
The Babylonians only worked in fractions of sixties. Some of the symbols of such fractions are the numbers 60, 602, 603, etc., such fractions as 1/7 could not be accurately expressed through sixties. They used these fractions approximately.
Ancient Rome emerged with its system of fractions. This system was divided into 12 sections of one unit, called ass. Twelve parts of an ass were called an ounce. They have the following names: “semіs” - half an ass, “sextani” - half an ass, “semіuncіya” - half an ass, then 1/24 ass. There were 18 different names of shot in the whole place. To work with such fractions, you need to remember both the addition table and the multiplication table. To make things easier, special tables were created. The downside of such a system was that it did not contain fractions from the symbols 10 or 100, which added up to 10, 100, etc. To understand the meaning of these difficulties, the Romans began to vicorize hundreds.
In walnut works, there were no fractions lost in mathematics, because The Greeks always respected the fact that mathematics must deal only with whole numbers. The Greek science began to have a lot of music.
The recording of fractions with a number and a sign was written in India, only the sign was written at the top, and the number at the bottom, and they also did not put between the fractions. The daily record of fractions was recorded by the Arabs. The foundation of the theory of prime fractions was laid by Greek and Indian mathematicians.
For the first time in Europe, the term was coined in 1202 by the first great mathematician of Central Europe, Leonardo of Pisa (1170 - 1250), better known as Fibonacci. A comprehensive theory of elementary fractions and the operation of them was developed in the 16th century by the Italian mathematician Niccolò Tartaglia (1499 - 1557) and the German and Italian mathematician, astronomer Christopher Clavius (Clav ія) (1537 - 1612). In ancient Russia, fractions were called fractions or numbers. The Russian term “fraction” is similar to the Latin word “fractura”, which translated from Arabic means “lamati”, “to fragment”. The term “fraction” is used in the “Arithmetic” of the Russian mathematician and teacher Leonty Pilipovich Magnitsky (1669 - 1739) both for prime and tens fractions.
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Recording fractions in Egypt The Egyptians tried to write down all fractions as sums of fractions, so that fractions have the form 1/n. For example, instead of 8/15 they wrote 1/3+1/5. Let's just say it's 2/3. Papyrus Ahmes has a command: “Divide 7 loaves among 8 people.” If you cut leather bread into 8 pieces, you will have to make 49 cuts. And in Egyptian the story went like this. The fraction 7/8 was written in the following form: 1/2 + 1/4 + 1/8. Well, every human being needs a portion of bread, a quarter of bread, and an eighth of bread; Therefore, the bread is cut in bulk, two loaves - into 4 pieces and one bread - into 8 pieces, after which each piece is given to each person.
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The Roman system of fractions and rounds was twelve. They sometimes say: “He has scrupulously applied his food.” This means that the nutrition has been completed to the end, so that the least amount of ambiguity is not lost. And the wonderful word “scrupulous” appears from the Roman name for 1/288 asses - “scrupulus”. The Roman system of fractions and rounds was twelve. They sometimes say: “He has scrupulously applied his food.” This means that the nutrition has been completed to the end, so that the least amount of ambiguity is not lost. And the wonderful word “scrupulous” appears from the Roman name for 1/288 asses - “scrupulus”. The following names were used: “semis” - half an ass, “sextans” - half of the fraction, “semiuncia” - half, then 1/24 of an ass, etc. Usyogo has 18 different names of fractions. To work with fractions, you need to store several fractions, an addition table, and a multiplication table. Therefore, the Roman merchants knew for sure that with the addition of triens (1/3 asses) and sextance it would cost sevens, and with the multiplication of a demon (2/3 asses) with a sessunction (3/2 ounces, or 1/8 assa) it would yield an ounce. To make the work easier, special tables were created, and their actions have come down to us.
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On the history of significant fractions Work from 6th grade student Kakurina Danila Kerivnik: Rozhko I.A.
Slide 2
And such a thing we have, All the stories about it, It is made up of numbers, And between them, like a place, Fractional rice lies, Above the devil there is a numberer, Know, Under the rice there is a signifier, Fractions like this inevitably need to be called primary.
Slide 3
Object of investigation: History of the origin of prime fractions Subject of investigation: Primary fractions Hypothesis: If there were no fractions, could mathematics have developed? The similarity of fractions - the consistency of the more detailed recording of fractions The question: perform an analysis: - why are fractions written in this way? - who came up with such notations? - what is their further development?
Slide 4
For a long time, the rich people of hundreds of peoples were called drib. The need for fractions began early in the development of mankind. So, perhaps, about a dozen fruits among a large number of participants in the field have stirred people up into pellets. The first shot was half. In order to take half from one, you need to divide one, or “break” it into two. The name of Lamania came here. Now they are called fractions. There are three types of fractions: single (aliquots) or fractions (for example, 1/2, 1/3, 1/4, etc.). Fractions are more systematic, in which the sign is expressed by the degree of the number (for example, by the degree of the number 10 or 60, etc.). I see, for some people, a number can be a number and a sign. real" - correct.
Slide 5
The first European figure who became a victor and expanded the current record of fractions was the Italian merchant and mandrel Fibonacci (Leonardo of Pisan). In 1202 centuries the word drib.
Slide 6
Fractions in Ancient Egypt.
The first shot was half. Behind her there were 1/4,1/8,1/16,..., then 1/3,1/6, then, then. The simplest fractions, parts of a whole, singular names. The ancient Egyptians identified all sorts of fractions in the form of sums other than the main fractions. The Egyptians wrote on papyrus, or on souvenirs, prepared from the stems of the great tropical plants that bore that same name. The most important place is the Ahmes papyrus, named after one of the ancient Egyptian scribes. By the hand of someone who wrote. Yogo dovzhina is 544 cm, and the width is 33 cm.
Slide 7
Preserved in London, at the British Museum. It was added to the last century by the English Rinda and is sometimes called the Rinda papyrus. This old mathematical document has the following headings: “The ways in which one can understand all the dark speeches, all the hidden things that are in speeches.”
Papyrus is a collection of 84 instructions that is of an applied nature; This task is carried out before working with fractions, the area of the rectum is determined, and also the arithmetic requirements for the proportional division, the ratio between the amount of grain and bread or beer that comes from oh, etc. Prote for the highest of these tasks is not given the same dirty rules , without even seeming to try any of the theoretical aspects.
Slide 8
Papyrus Ahmes has a task - to distribute this bread equally among all the people.
The current student has learned for everyone that the instructions are like this: the requirement is to cut the skin bread into 8 equal pieces and each person should cut one piece of the skin bread. And the axis of this promise is written on papyrus: Every person needs half, a quarter and an eighth of bread. Now it is clear that you need to cut 4 loaves of bread in half, 2 loaves of bread into 4 pieces and just one loaf of bread - into 8 pieces. And since our student had the opportunity to earn 49 roses, then Ahmes - only 17, then. The Egyptian method is even more economical.
Slide 9
To sort out different fractions from the sum of single fractions, ready-made tables were used, which were used to calculate the Egyptian censuses of necessary calculations.
This table helped to perform complex arithmetic calculations according to the accepted canons. Obviously, the scribes taught them to memorize, just as schoolchildren memorize the multiplication table. Following this table, a subset of numbers was added. The Egyptians also multiplied and divided fractions. To multiply, I had to multiply the parts by parts, and then, perhaps, I’ll recreate the table. It was even more folding on the right side of the split.
Slide 10
Babylon.
In ancient Babylon, a high level of culture was reached in the third millennium BC. The Sumerians and Akkadians, who inhabited Ancient Babylon, wrote differently on papyrus, which is not rice in the country, but in clay. By pressing a wedge-shaped stick on the soft clay tiles, marks were made to make the wedges less visible. Why is such a sheet called cuneiform?
Slide 11
The vertical wedge is marked 1; 60; 602; 603,...Horizontal wedge marked 10. To write 62 we found it like this: gap
Slide 12
Fractions in Ancient Rome.
The Tsikava shot system was in Ancient Rome. Vaughn was grounded on a division into 12 parts of one vaga, which was called as. The twelfth part of an ace was called an ounce. And along the way, sometimes other magnitudes matched the night river - the car. For example, the Roman could say that he had passed this ounce of a book, or had read five ounces of a book. In this case, obviously, there was no mention of the name of the nobleman or the book. I am glad that 7/12 of the route has been completed or 5/12 of the book has been read. And for fractions that come out as shortened fractions with the sign 12 or fragmentation of twelve parts into fractions, there were special names.
Slide 13
The Roman system of fractions and rounds was twelve. They sometimes say: “He has scrupulously applied his food.” This means that the nutrition has been completed to the end, so that the least amount of ambiguity is not lost. And the wonderful word “scrupulous” appears from the Roman name for 1/288 asses - “scrupulus”. The following names were used: “semis” - half an ass, “sextans” - half of the fraction, “semiuncia” - half, then 1/24 of an ass, etc. Usyogo has 18 different names of fractions. To work with fractions, you need to store several fractions, an addition table, and a multiplication table. Therefore, the Roman merchants knew for sure that with the addition of triens (1/3 asses) and sextance it would cost sevens, and with the multiplication of a demon (2/3 asses) with a sessunction (3/2 ounces, or 1/8 assa) it would yield an ounce. To make the work easier, special tables were created, and their actions have come down to us.
Slide 14
Ancient Greece.
There were no fractions lost in the Greek works of mathematics. The Greeks always respected the fact that mathematics can deal with only whole numbers. Merchants, craftsmen, as well as surveyors, astronomers and mechanics were left to deal with the stink shot. Once upon a time it was said: “Drive nature at the door, let it fly in at the window.” That’s why fractions penetrated into the strictly scientific works of the Greeks, so to speak, “from the back.” In Greece, orders from single, “Egyptian” fractions and zagalny, simple fractions were used. Among the various records, the following was used: to the beast there is a sign, under it there is a number of fractions.
Slide 15
Even 2-3 centuries before Euclid and Archimedes, the Greeks had mastered arithmetic methods with fractions. At VI Art. BC The famous Pythagoras is alive. They say that how many students go to his school, Pythagoras Vidpoviv: “Half of them study mathematics, the other half study music, and the other half study at home, in addition to three wives.”
Slide 16
Fractions in Russia.
In Russia, fractions were called fractions, later “laman numbers.” For example, fractions were called generic or basic. Half, half –1 2 Half – 1 4 Half – 1 8 Half half – 1 16 P’yatina – 1 5 Tretina – 1 3 Pivtretina –1 6
Slide 17
The history of the assignment of fractions.
A modern system for recording fractions using numbers and numbers was created in India. Only the people there wrote the sign of the fire, and the numberer - below and wrote shot rice. The Arabs began to write fractions exactly like this. In Ancient China, they used a dozen system of entries, designated by other words, vikoryst entries of dozhin chi: tsuni, chastka, order, wool, thinnsha, cobweb. The fraction is 2.135436, looking like this: 2 chi, 1 tsun, 3 parts, 5 ordinal, 4 hairs, 3 thinners, 6 spiders. In the 15th century, in Uzbekistan, the mathematician and astronomer Jamshid Giyaseddin al-Kashi wrote down the fractions in one row as numbers in the tens system and gave rules for dealing with them. Vin koristuvavsya dekilkoma ways of writing fractions: either by stastouvuv vertical border, or ink black and red colors.
Slide 18
Ancient treasures with fractions.
The work of the famous Roman poet of the 1st century BC. e. Horace described the conversation between a teacher and a student in one of the Roman schools of that era: Teacher. Tell me, son Albina, how much will you lose if you take one ounce from five ounces? Learn. One third. Reader. Right. You can take care of your mainno. Resolution: 4 oz. 4 oz. 4 oz. Version: 1/3
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Zavdannya from the "Papirus of Ahmes" (Egypt, 1850 BC)
"A shepherd comes with 70 cows. They feed him: - How many of your flock do you bring? The shepherd says: - I bring two-thirds to a third of thinness. Respect!" Solution: 1) 70:2 · 3 = 105 goals - that's 1/3 of leanness 2) 105 · 3 = 315 lean goals Type: 315 lean goals
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Thank you for your respect!
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Literature
1. History of arithmetic. Depman, born 1965 2. History of mathematics from Descartes to the mid-19th century. Vileitner, 1960. 3. Encyclopedia for children Avanta + mathematics. 4. Children's Encyclopedia. M., 1965.
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