Ancient abacus 4 letters crossword puzzle. History of the development of computer technology - manual stage - abacus

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Abacus(ancient Greek ἄβαξ, ἀβάκιον, lat. abacus - board) - counting board, used for arithmetic calculations from approximately the 5th century BC. e. in Ancient Greece, Ancient Rome.

Antique period is a conventional period of historical time that covers the period from 1 thousand years BC to the 1st millennium AD. Historians mark this era as the heyday of the slave system, which replaced the primitive communal one.

The ideal location of the Greek territory relative to the Mediterranean, Aegean, Black and Marmara seas, as well as the mild climate, actively contributed to the successful development of not only various crafts, but also trade with neighboring countries.

It should be noted that the administrative structure of the country was unique at that time - the bulk of the population with a high level of income was concentrated in large cities - policies, which, in fact, were separate states. The policies subjugated smaller settlements that supplied the city with agricultural products, household items, and construction materials.

To carry out trade between cities, a special, unified unit was required through which the value of all goods would be expressed. Barter could not always satisfy the interests of both parties, so it was replaced by money, which took the form of plates of precious metals - gold and silver. The disadvantage of the system was that each policy had its own money, which often differed in denomination, weight, and shape. It was necessary to make complex calculations in order to bring the trading result under a common denominator, and it was almost impossible to do this quickly, without using a counting system.

Counting money, and then usury, was carried out by a select category of citizens of the policy, who enjoyed great authority and respect among other residents of the city. Over time, the number of transactions carried out by them increased - moneylenders not only engaged in intermediary in financial transactions, but also exchanged money, accepted it for safekeeping, gradually evolving into bankers. At first, all the necessary records and calculations were made on wooden tablets or papyrus. Which at that time was an unaffordable luxury, and spending it on calculations even of national importance was unnecessary waste. In order to speed up arithmetic operations, 2500 years ago an unknown inventor invented an easy-to-make device - the abacus.

The history of abacus

Ancient Greece gave the modern world many important and life-making inventions, one of which is rightfully considered the abacus. This simple device, designed for carrying out simple mathematical calculations, appeared around the 5th century BC, and was a wooden or stone tablet with slots in which pebbles made of wood or marble moved freely along certain grooves.

The oldest abacus that has survived to this day was discovered during excavations on the island of Cyprus, in the vicinity of the largest and fortified city of Salamis. The find dates back to 300 BC, and it looks like a plate of white marble, and its dimensions are quite impressive. The length of the abacus is almost one and a half meters, width - 75 cm. The thickness of the marble plate is 4.5 cm. The abacus has a complex system of slots along which stone balls moved. The exact purpose of the device is not known for certain, but judging by its size and weight, it served to calculate taxes or expenses from the city budget, and was installed near the Salamis treasury.

Economy of Ancient Greece

Researchers of the history of the Ancient period of the development of Greece often have an interest in such an everyday aspect as the economic relationships of cities and their individual inhabitants with each other.

It is worth noting the rather interesting views of the inhabitants of Hellas on financial responsibility. Theft in Ancient Greece or embezzlement of the state budget was considered by them solely as an economic crime, the punishment for which was full compensation for the shortage by the financially responsible person. The theft of money from the policy treasury was punishable by compensation of losses tenfold, so it was profitable for some cunning individuals to put a wealthy city resident in the place of a banker, and then frame him and accuse him of embezzlement. Thus, the newly minted banker was forced to compensate for the damage, while losing his own property.

The system of bank records about various transactions was carried out by applying marks on wooden planks in chronological order, without any systematization. From time to time, in order to compile a report for a month or a year, it was necessary to do additional work - recapitulation, which consisted of re-verifying the records and establishing their chronology. To make the already difficult work of bankers easier, abacuses were used. Probably, at first they looked like ordinary small pebbles - river or sea pebbles of the same size, with smooth, rounded outlines. By the way, the very word “ calculation", comes from the Latin " calculos", which meant small pebbles. This is probably where the modern name for river and sea sediments comes from - pebbles.

It was very inconvenient to use pebbles in a large number of monotonous calculations, since they constantly fell off the table, got lost, or rolled from one pile to another, which greatly reduced the accuracy of the operations. In order to make accounting of money and material resources more perfect, a currently unknown inventor took a marble tablet, made slits in it, and placed 10 pebbles in them, allowing them to move freely along the grooves. Such a tool could always be taken with you and used to control the consumption of materials on construction sites, calculate the amount of taxes for traders who came to the city, and record revenues to the state treasury.

The system of storing public funds in the policies of Ancient Greece was interesting. Each type of income received was distributed as follows: several large jugs with letter indices were kept in a special secure room. Each jug separately contained funds received from specific activities - taxes from traders, income taxes, payments received from ships in ports, and other duties. Financing for these industries came from the same pot, so the overall balance of expenses was not disturbed.

The keys to the room with the money itself were kept by one banker, and to the room with all the documentation - by the second. The exchange of keys was strictly prohibited, as a result of which protection against deliberate embezzlement was quite high.

Taxation system of Ancient Greece was arranged surprisingly well. When paying duties, not only arithmetic was born, but also the method of linear or positional notation. Banking records were also well organized. Each contribution or disbursement of funds could be made in cashless form, and all financial movements were carefully recorded and could be made public in the business center of the policy - the agora.

Maintaining such detailed reports was impossible without the abacus. They were distributed everywhere - in banks, which were then called “trapez”, in government agencies and ports.

Analogues of abacus in world history

Such an important invention as the abacus arose long before the advent of in Greece, although it was in Hellas that it acquired modern features. The first known mention of abacus is preserved in documents of Ancient Babylon, which date back to the 3rd millennium BC. The Babylonian abacus looked like a horizontal board with recesses made in it, along which pebbles or other small objects moved. Later, 500 years BC, the Egyptians improved the design, using not recesses, but sticks or copper wire, on which rosary beads made of clay, wood or stone were strung. This solution made it possible to use the abacus not only horizontally, which was often inconvenient, but also vertically.

After the appearance of abaca in Greece, Arabs and Indians became acquainted with the invention. They also brought abacus to Western Europe, capturing Spain in the 8th century. Here the abacus changed somewhat - instead of pebbles, they began to use metal tokens on which Roman numerals or symbols - apexes - were applied. State treasury settlements using abacus were carried out in Europe until the 18th century, after which they were replaced by more productive methods of algorithmization.

Eastern countries such as China and Japan also actively used abacus. The Chinese counterpart was called suanpan, and the Japanese counterpart was called soroban. They practically did not differ from each other in design, which proves their common origin. Suanpan had 10 categories - according to the number of fingers on the hands, and two vertical columns - according to the number of hands, and was intended for simple calculations of household, industrial, construction and financial plans. The Chinese and Japanese abacus is not just a device for facilitating arithmetic operations, but also a whole art. In Japan, counting on the soroban is still officially included in the school curriculum, and working with it is not just a tribute to tradition or fashion, but also has purely practical significance. Despite the large number of modern electronic devices, many small entrepreneurs, sellers in stores and markets prefer to use abacus in everyday life. Well-developed action algorithms allow you to perform all basic mathematical operations on suanpan and soroban - addition, subtraction, multiplication and division, as well as raising to powers and extracting square and cubic roots.

Russian abacus makes it possible not only to add and subtract various numbers, but also to work with quarters, tenths and hundredths. The appearance of abacus in Russia dates back to the 15th-16th centuries. The active spread of abacus continued until the end of the twentieth century, when such devices were replaced by more accurate electronic calculators. Until the early 1980s, teaching arithmetic operations on the abacus was part of the school curriculum for Soviet schoolchildren.

Abacus in Ancient Greece replaced the old-fashioned finger counting, which required additional steps. The development of the technique made it possible to make calculations fast, accurate and easy. Each pebble on the abacus could mean units, tens, hundreds, thousands, which significantly expanded the scope of the instrument. There was even a widespread joke about this in Hellas: “A courtier is like an abacus pebble: if he wants a counter, the price will be a whole talent, but if he wants it, only a halq.”

It is safe to say that the invention of the abacus gave a strong impetus not only in relation to monetary transactions and trade, but made it possible to make complex calculations in the construction of ancient temples and other architectural objects that we can enjoy to this day.

The history of digital devices should begin with abacus. A similar instrument was known among all nations; let’s look at some of them.

Abacus(Latin abacus - board) - a counting board used for arithmetic calculations.

It probably first appeared in Ancient Babylon around 3 thousand BC. e. Originally it was a board cut into strips or with indentations made. Counting marks (pebbles, bones) moved along lines or depressions. In the 5th century BC e. in Egypt, instead of lines and indentations, they began to use sticks and wire with stringed pebbles.

Ancient Greece

The ancient Greek abacus (board or "Salaminian board" named after the island of Salamis in the Aegean Sea) was a plank sprinkled with sea sand. There were grooves in the sand, on which numbers were marked with pebbles. One groove corresponded to units, the other to tens, etc. If more than 10 pebbles were collected in any groove when counting, they were removed and one pebble was added in the next rank.

Ancient Rome

The Romans improved the abacus, moving from wooden planks, sand and pebbles to marble planks with chiseled grooves and marble balls.

China

The Chinese abacus suan pan consisted of a wooden frame divided into upper and lower sections. The sticks correspond to the columns, and the beads correspond to the numbers. For the Chinese, counting was based not on ten, but on five. Suan-pan are divided into two parts: in the lower part on each row there are 5 stones, in the upper part - 2. Thus, in order to set the number 6 on these abacus, first put the stone corresponding to the five, and then added one bone in the units category.

Japan

The Japanese called the same device for counting serobyan. Serobyan is a Japanese abacus, descended from the Chinese suan-pan, which was brought to Japan in the 15th - 16th centuries. Serobyan is simpler than his predecessor; he has one less ball on his “palate” than suan-pan.

Europe

In Europe, abacus was used until the 18th century. Even the development of mathematics itself at certain stages of its formation was associated with the abacus, when the truth of some computational algorithms was confirmed by the possibility of their implementation on the abacus. In the Middle Ages, supporters of performing arithmetic calculations exclusively with the help of abacus - the abaciists - for several centuries waged a fierce struggle with algorithmists - adherents of the methods of algorithmization of arithmetic operations that arose at that time.

Russia

In Rus', for a long time, they counted by bones placed in piles. Around the 15th century, the “plank bill” became widespread, apparently imported by Western merchants with blubber and textiles. The “board abacus” was almost no different from ordinary abacus and consisted of a frame with reinforced horizontal ropes on which drilled plum or cherry pits were strung.

Modern abacus

The centuries-long path of improvement of the abacus led to the creation of a calculating device of a complete classical form, used until the heyday of keyboard desktop computers, we call it “abacus”.

An abacus is a simple mechanical device for performing arithmetic calculations, which is one of the first computing devices. The abacus is a frame with knuckles strung on knitting needles. In the recent past, they were used everywhere in the USSR. Moreover, even today in some places you can find them helping in settlement transactions. And only the advent of pocket electronic calculators in the 70s of our century created a real threat to the further use of Russian, Chinese and Japanese abacus - the three main classical forms of the abacus that have survived to this day.

Ancient abacus

Board for arithmetic calculations in Ancient Greece, Rome, then in Western Europe until the 18th century.

Architectural detail: slab above column

Upper part of a column capital

A board that was used in ancient times for arithmetic calculations

Computer of the ancient world

Ancient counting board

Prehistoric computer

Accounts of ancient accountants

Antique abacus

Pythagorean calculator

Greek abacus

Ancient counting board

The first article of the “Mathematical Encyclopedic Dictionary” is devoted to this subject.

Ancient abacus with quinary number system

The history of the computer begins with this calculating device

Antique computer

In architecture, the top of a column capital

Pilaster top plate

Arithmetic board in Ancient Greece

Stone Age calculator

Abacus of the Hellenes

Abacus from Ancient Greece

Counting board

Part of a column capital

Ancient abacus

Great-great-grandfather of the computer

Archimedes' abacus

Ancient "arithmometer"

Ancestor of the calculator

Upper part of the capital

Antediluvian abacus

Accountants' Knuckles

Ancient mathematicians board

Board with pebbles

Greek "board"

Hellenic counting board

Top of the column

Slab on top of capital

Ancient "calculator"

Slab over column

The most ancient abacus

Greek ancestor of the calculator

Antique counting board

Ancient Greek pebbles that love counting

Pythagorean times calculator

Ancient counting board

Ancestor of stationery accounts

Top of the capital

In Rus' there is an abacus, but in Greece?

Antediluvian abacus of the ancient Greeks

Abacus for Pythagorean calculations

Computer from the time of Daedalus and Icarus

Analogue of accounts among the ancient Greeks

The oldest abacus

Forefather of the computer

Prototype of accounts

Abacus from the times of Pythagoras

Distant ancestor of the calculator

Antique "calculator"

Accounts from the times of Daedalus and Icarus

Abacus of ancient times

An ancient calculating device

Ancient counting board

Archaic counting board

Accounts of our ancestors

Old abacus

. Archimedes' "arithmometer"

Vintage abacus

Ancient Greek abacus

The counting board of the ancient Romans

Upper plate of column capital, pilasters

Pythagorean calculator

Is it possible to imagine a world without numbers? Remember what you and I do every day: without numbers you can’t make a purchase, you can’t find out the time, you can’t dial a phone number. And spaceships, lasers and all other achievements! They would simply be impossible if it were not for the science of numbers. When answering the question “how much?”, we almost always name one number or another. Number is one of the basic concepts of mathematics, allowing one to express the results of counting or measurement.

In past times there were many ways of counting. The art of counting has evolved with the development of humanity. In those days, when a person only collected fruits in the forest and hunted, he only needed his hand to count. Our fingers are always with us.

The human hand is the first “calculating machine”. The boy drove out the herd, bent his fingers, and when he drove the goats, he again counted them on his fingers and compared whether he had bent all his fingers. Fingers were the first conventional symbols for designating numbers. This is how the idea of ​​using fingers to represent numbers was born. When the fingers on one hand ran out, they moved to the other, and if there weren’t enough on both hands, they moved to their feet. Therefore, if in those days someone boasted that he had “two arms and one leg of chickens,” this meant that he had fifteen chickens, and if it was called “the whole man,” that is, two arms and two legs, this meant twenty.

When many animals took part in the counting, the fingers ran out, and the question arose of how to designate the tens. Then they turned to nicks and pebbles.

In ancient times, when a person wanted to show how many animals he owned, he would put as many pebbles in a large bag as the number of animals he owned. The more animals, the more pebbles. This is where the word “calculator” comes from, “calculus” means “stone” in Latin!

With the development of man, trade arose and merchants appeared. In order to count how many goods he purchased, it became necessary to perform operations with numbers. For example, count the number of bags of cereal and flour. To do this, they began to use two grooves in the sand and a bag of pebbles. The right column represents units, and the left column represents tens. Place five pebbles in the right groove. Each of them represents one bag of cereal. And put four pebbles in the left groove. Each will represent a dozen bags. The pebbles in both grooves will show that you have 4 dozen and 5 more bags - a total of 45. You indicated the number of grains purchased by the merchant at the market. To add 43 bags of flour, add three pebbles to the right groove and four to the tens groove. By counting the pebbles in the grooves, the answer is that the merchant bought 88 bags in total.

While counting the goats, the shepherdess, having counted all the fingers on her hands, put one pebble aside, and then continued counting from hand to hand. With every ten, she put aside a pebble, when the herd came out of the pen, there were 4 pebbles lying on the ground and eight fingers turned out to be bent. Thus, she put 48 goats out to pasture.

When Robinson Crusoe in the book by the writer Defoe remained on a desert island, he kept a kind of calendar. To do this, he made a short notch on a post dug into the ground every day, and every 30 days he made a longer notch. This is how Robinson counted the days and months spent on the island.

In Russia, the expression has been preserved: “Cut it on your nose.” It says that in order to remember something important, you should make a note. The word “nose” in this case is derived from the word “to wear.” In the old days, many people carried small sticks with them for notching. They called them “nose”, and in order to remember the required number, they made the corresponding number of notches on the “nose” - marks.

Serifs on sticks were used in trade transactions. After completing the payments, the sticks were broken in half, one half was taken by the creditor, and the other by the debtor. The half played the role of a “receipt”.

The Peruvian Incas kept track of animals and crops by tying knots on straps or laces of varying lengths and colors. These bundles were called kipu. Some rich people accumulated several meters of this rope “counting book”, try it, remember in a year what 4 knots on a string mean! Therefore, the one who tied the knots was called a rememberer

Rope abacus with knots were in use in Russia, as well as in many European countries. People still sometimes tie knots on handkerchiefs as a keepsake.

Figures of ancient civilizations

Numbering of the ancient Sumerians

The ancient Sumerians were the first to come up with the idea of ​​writing numbers. They only used two numbers. A vertical line denoted one unit, and an angle of two recumbent lines denoted ten. They made these lines in the form of wedges, because they wrote with a sharp stick on damp clay tablets, which were then dried and fired.

What was the Mayan number system?

The ancient Mayan people, instead of the numbers themselves, drew scary heads, like those of aliens, and it was very difficult to distinguish one head - a number - from another.

At the beginning of our era, the Mayan Indians, who lived on the Yucatan Peninsula in Central America, used a different number system - base-20. They denoted 1 with a dot, and 5 with a horizontal line, for example, the entry == meant 14. The Mayan number system also had a sign for zero. In its shape it resembled a half-closed eye.

It is interesting that different peoples living in countries distant from each other and at different times invented their own methods for writing numbers, but still somewhat similar to other ways of writing numbers.

What were the Egyptian numbers like?

The Egyptians wrote in hieroglyphs, that is, they used drawings to represent an idea or object. These drawings depicted elements of the flora and fauna of the Nile River and household utensils. They also wrote numbers in hieroglyphs. The Egyptians had signs to represent numbers from 1 to 10.

In ancient Egyptian numbering, which originated more than 5,000 years ago, there were special characters for writing the numbers 1, 10, 100, 1000, ... and a special hieroglyph for tens, hundreds of thousands, tens of thousands, hundreds of thousands, millions and tens of millions. At that time, only specially trained people could write and count; for ordinary people, counting was just as inaccessible as writing. This system was used in Ancient Egypt for trade and tax collection, especially widespread during the construction of the Great Pyramids, and gradually died out along with the caste of builders and accountants during the decline of Egypt.

In order to depict, for example, the integer 23145, it is enough to write in a row two hieroglyphs representing ten thousand, then three hieroglyphs for a thousand, one for a hundred, four for ten and five hieroglyphs for one: .

Babylonian wedges

The Babylonian peoples used only two cuneiform signs - a straight wedge and a lying wedge. These peoples used a sexagesimal number system, for example the number 23 was depicted like this: The number 60 was again indicated by a sign, for example the number 92 was written like this:

Ancient Greece and Rus'

The ancestors of the Russian people - the Slavs - used letters to designate numbers. Above the letters used to designate numbers, special signs were placed - titla. To separate such letters - numbers from the text, dots were placed in front and behind. This method of designating numbers is called tsifir. It was borrowed by the Slavs from the medieval Greeks - the Byzantines. Therefore, numbers were designated only by those letters for which there are correspondences in the Greek alphabet.