History of the development of computer technology - manual stage - abacus. History of the development of computer technology - manual stage - abacus Abacus from time immemorial 4 letters

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.

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

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

Ancient abacus

Upper plate of column capital, pilasters

Pythagorean calculator

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

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