___domain___ Secrets of magic.
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TARGET:
Find out the history of numbers in different countries
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Primitive people did not know counting. They had no one to learn from. Their teacher was life itself. Observing the surrounding nature, on which his life completely depended, our distant ancestor first learned to isolate individual objects from many different objects. From a flock of wolves - the leader of the pack, from a herd of deer - one deer, from a brood of swimming ducks - one bird, from an ear of grain - one grain. At first they defined this relationship as “one” and “many”. Frequent observations of sets consisting of a pair of objects (eyes, ears, horns, wings, hands) led man to the idea of number. Our distant ancestor, talking about seeing two ducks, compared them to a pair of eyes. And if he saw more of them, he said: “Many.” Only gradually did people learn to identify three objects, and then four, five, six, etc. How did people learn to count?
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Life required learning to count. To get food, people had to hunt large animals: elk, bear, bison. Our ancestors hunted in large groups, sometimes with the whole tribe. For the hunt to be successful, it was necessary to be able to surround the animal. Usually the elder placed two hunters behind the bear’s den, four with spears against the den, three on one side and three on the other side of the den. To do this, he had to be able to count, and since there were no names for numbers then, he showed the number on his fingers. And by the way, feet and fingers played a significant role in the history of counting, especially when people began to exchange objects of their labor with each other. So, for example, wanting to exchange a spear with a stone tip that he had made for five skins for clothing, a man would put his hand on the ground and show that a skin should be placed against each finger of his hand. One five meant 5, two meant 10. When there were not enough arms, legs were used. Two arms and one leg - 15, two arms and two legs - 20. There were special names for numbers - at first only for one and two. Numbers greater than two were named using addition: 3 is two and one, 4 is two and two, 5 is two, two more and one.
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How did people learn to write numbers?
This was done differently in different countries and at different times. When people did not yet know how to make paper, notes appeared in the form of notches on sticks and animal bones, in the form of shells or pebbles set aside, or in the form of knots tied on a belt or rope. ...In one of the drawings, a man raised both hands up. He had something to be surprised about. After all, it meant a whole million. And it's not a joke. The ancient Egyptians drew such a man when they wanted to depict a million. The little man performed the duties of a number. Now we, accustomed to writing numbers, cannot even believe that there was any other system for writing numbers. These “figures” were very different and sometimes even funny among different peoples. In Ancient Egypt, the numbers of the first ten were written with the corresponding number of sticks. And “ten” was indicated by a bracket in the shape of a horseshoe. To write 15, you had to use 5 sticks and 1 horseshoe. And so on up to a hundred. For hundreds, a hook was invented, for thousands, an icon like a flower. Ten thousand was indicated by a finger pattern, one hundred thousand by a frog, and a million by the familiar figure with raised hands. It was not very convenient to write large numbers in this way and it was completely inconvenient to add, subtract, multiply, and divide them. There was a lot of fuss with these hieroglyphic icons!
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Around the third millennium BC, the Egyptians came up with their own numerical system, in which special icons - hieroglyphs - were used to indicate the key numbers 1, 10, 100 and so on.
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The size of the number did not depend on the order in which its constituent characters were located: they could be written from top to bottom, from right to left, or mixed
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Ancient Egypt figures
1 10 100 100 000 10 000 1 000 000 1000 1
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The numbers were made up of these key symbols by addition: 3 2 5 2
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A much better way to write numbers was in ancient Babylon. It is very similar to the modern one, only we count in tens, hundreds, thousands and so on, but the inhabitants of ancient Babylon united units of 60, 3600 (60x60=3600), and if necessary, 60x60x60=216000 and so on. In ancient Babylon they wrote on soft clay tablets with sharp sticks, and then the tablets were fired, and they became hard and durable. During excavations, entire libraries and archives of such tablets were found. It is difficult to depict complex figures with a stick on clay, so Babylonian writing consisted mainly of various combinations of wedges (it is called cuneiform). Units were represented by narrow vertical wedges, and tens by wide horizontal ones; all numbers up to 60 were “collected” from such wedges. When it was necessary to write down a number greater than 60, then the next digit was opened - they wrote in it how many times the number 60 fits in the number being written down, and what remained (that is, the remainder of division by 60) was written down as before , in the first category. Spaces were left between the digits so that numbers from different digits did not mix. This notation of numbers is convenient because if we know how to multiply and add numbers of the first digit, then it is very easy to learn how to perform these operations with any numbers - these calculations can be carried out “in a column”, as you are taught at school. True, the Babylonian system was still very cumbersome due to the fact that 60 is a rather large number, so it was not used anywhere else. But the system of numbering and calculations, which developed in India around the 6th century AD, turned out to be so convenient and successful that it is now used all over the world. Europeans became acquainted with it in the 10th - 13th centuries through the Arabs, who were the first to appreciate the merits of this method of writing numbers, adopted it and transferred it to Europe, so new numbers in Europe began to be called Arabic. This also happened because the simplest calculating device, operating in the decimal number system, was always at hand - these are his 10 fingers.
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ARABIC NUMERALS
0, 1, 2, 3, 4, 5, 6, 7, 8, 9. They were invented a long time ago, back in the sixth century, in India; but the numbers are called Arabic because they came to Europe from the Arabs. In Russia, Arabic numerals began to be used under Peter I. Each digit represents a single digit number. Numbers made up of two digits are called two-digit numbers, and numbers made up of three digits are called three-digit numbers.
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ROMAN NUMERALS
There are only seven of them: Unit - I Five - V Ten - X Fifty - L Hundred - C Five Hundred - D Thousand - M Rules for reading and writing numbers: Read numbers written in Roman numerals from left to right. If a larger digit is written before a smaller one, then when reading, their values are added together. In this case, the same number can be repeated two or three times.
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Contents How we count Abacus in different countries Methods of counting Finger counting The origin of numbers
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As we believe, the art of counting has developed with the development of humanity. In those days, when a person only collected fruits in the forest and hunted, four words were enough for him to count: one, two, three and many. This is exactly what some tribes living in the jungles of South America still believe.
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However, when people began to engage in animal husbandry and agriculture, it became necessary for them to count the goats in the herd or the number of baskets with grown fruits (of which there were more than three) stored for the winter.
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If more than 10 pebbles were collected in any groove when counting, they were removed and one pebble was added in the next rank. The Romans improved the abacus, moving from wooden planks, sand and pebbles to marble planks with chiseled grooves and marble balls.
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The so-called “Vestonitsa bone” with notches was discovered in excavations. This allows historians to assume that already 30 thousand years BC. our ancestors were familiar with the rudiments of counting.
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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.
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Abacus in different countries 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 numbers. For the Chinese, counting was based not on ten, but on five.
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It is divided into two parts: in the lower part there are 5 seeds on each row, in the upper part there are two. Thus, in order to set the number 6 on these abacuses, they first placed the bone corresponding to the five, and then added one to the units digit.
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In Rus', for a long time, they counted by bones placed in piles. Around the 15th century, the “plank count” became widespread. 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. "Russian Schot"
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Methods of counting Many methods of counting were invented: notches were made on a stick according to the number of objects, knots were tied on a rope, pebbles were piled up. But you can’t take a stick with notches with you, and it’s not very pleasant to carry stones, and the shepherd needs to know if any goat has strayed from the herd.
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And here fingers come to the rescue - an excellent counting material, it is still used not only by first-graders. What if there are more than ten items?
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Thus, to express the number “twenty,” South American Indians contrast their fingers with their toes.
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Of course, you can use your toes, but what next? There was nothing left to do but come up with the decimal system that we use now: we count tens; when there are ten tens, we call them a hundred; then ten hundred - a thousand.
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The “finger” origin of the decimal system is confirmed by the shape of the Latin numerals: the Roman numeral five (V) is a palm with a protruding thumb, and the Roman numeral ten (X) is two crossed hands. Finger counting.
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The Mayan Indians in America counted in fives: one five is a unit of the next category, five fives is a new category, etc. It is clear that they only used the fingers of one hand.
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Some tribes used only four fingers of one hand, but they took into account that each finger consists of three phalanges, i.e. they had twelve counting objects at their disposal
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This is how the dozen arose, which a hundred years ago was widespread in both Europe and Russia, but gradually gave way to the ten. Until now, in Europe, buttons, handkerchiefs, chicken eggs, and much more that are sold individually are considered dozens.
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Everyone knows that a thousand thousand is a million. A thousand millions is called a billion or a billion (“bi” means two in Latin). A thousand billion, i.e. 1,000,000,000,000 – trillion (“three” - in Latin – three), then 1,000,000,000,000,000 – quadrillion (quadra – four), then quintillion, sextillion, octillion, nonillion decillion.
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Large numbers arise in astronomy, they often talk about “astronomical numbers”, since the masses of stars and the distances between them are expressed in really large numbers, but physicists have calculated that the number of atoms - the smallest particles of matter - in the entire Universe does not exceed the number expressed by one followed by hundred zeros . This number received a special name - googol.
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The emergence of numbers. We are accustomed to using the benefits of civilization - a car, telephone, TV and other equipment that makes our life easier and more interesting. Thousands of inventions were required for this, but the most important of them were the first ones - the wheel and the number. Without them, all our technical splendor would not exist. It would seem that the concept of number should arise simultaneously with the ability to count, but this is far from the case.
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It has been noticed that both cats and pigs can count to five, but in order to move from five objects to the number “five”, a great discovery was required, and here’s why. Five dogs or five pigs are not at all the same as five nuts.
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Five dogs or five pigs are not at all the same as five nuts. After all, five nuts are very few, you ate them and didn’t notice, but five pigs are a lot, enough to feed a large family for a long time. Five dogs are a pack that can provide good protection from wild animals, but five fleas on a dog are difficult to see. Is it possible to compare them?
