Most people remember from school that ancient people believed that the Earth was flat. We were told about this in both history and geography lessons. Overall, this is a very common fact that most people know equally well. modern people. But that's why people in ancient times believed that the Earth was flat, that's enough interest Ask. And today we will figure it out.
Mythology
First of all, one of the weighty arguments for most people in ancient times, which argued in favor of the fact that our planet is flat, were all kinds of myths and beliefs.
Different cultures have had all sorts of legends about what our planet is like, and people have believed and followed them for generations. For example, one of the most widespread and well-known legends to us today is the hypothesis that the Earth supposedly stands on four elephants, which are located on a turtle. In addition, the turtle itself, in turn, was located on a snake curled into a ring.
Of course, today such a hypothesis seems absurd to us, but many centuries ago people believed in it, and if we talk about the entire history of our planet, which goes back millions of years, then we are confident that the Earth is spherical not so long ago.
Rational grain
However, in the assumption that the Earth is flat, in which ancient people were confident, there is also a rational grain located on the very surface of the issue.
The point is that any ancient person, standing on earth, could look in front of him and see only the endless expanses of the planet, which continue all the way to the horizon. In those days, of course, there were no skyscrapers or even two-story houses, so the only obstacles to the human gaze could only be trees and mountains. All that people saw in front of them was endless nature stretching out in front of them. And, as you understand, it stretched exclusively in a straight line.
That is why people could not even think that the Earth was a ball, because the fact that it was flat seemed an absolutely rational and indisputable fact. Moreover, the plane of the planet was confirmed by numerous myths and legends that people encountered in different cultures and in different parts of our planet.
This is the answer to the question of why people in ancient times believed that the Earth was flat.
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What did ancient people think? Prepared by: Sofya Kislyakova, 5B grade student Mathematics teacher: O.A. Mosunova Truth is not lost in counting (Russian proverb)
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Objectives Study the literature on this issue Find out the history of the emergence of modern numbers What they used for counting. To study how people of different nations believed in ancient times.
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Main research methods: literature analysis, comparison, survey of students, analysis and synthesis of data obtained during the study.
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Hypothesis I think is not used anywhere in modern world account of ancient people
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Plan Discussion of the topic Search for information Conducting a student survey Summing up the survey Conclusion
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Primitive people The life of primitive people was not much different from the life of animals. And people themselves differed from animals only in that they spoke and knew how to use the simplest tools: a stick, a stone or a stone tied to a stick. Primitive people, like modern small children, did not know counting. Their teacher was life itself. Therefore, training went slowly. 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 flock, from a herd of deer - one deer, from a brood of swimming ducks - one bird, from an ear of grain - one grain
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Primitive people The first concepts of mathematics were less, more and the same. When one tribe exchanged its fish catch from another for stone knives, there was no need to count how many fish and how many knives they brought. They simply placed a knife next to each fish. Until recently, there were tribes whose language had the names of only two numbers: one and two. They counted like this: 1 - "urapun" 2 - "okosa" 3 - "okosa-urapun" 4 - "okosa-okosa" 5 - "okosa-okosa-urapun" All other numbers were called "many"!
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First counting 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 a person learn to identify three objects, and then four, five, six, etc. By the way, 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) Traces of counting on the fingers have been preserved in many countries.
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So in China and Japan, household items (cups, plates, etc.) are counted not by dozens and half dozens, but by fives and tens. In France and England, counting in twenties is still in use. At first there were special names for numbers 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. The names of numbers among many peoples indicate their origin. So the Indians have two - eyes, Tibetans - wings, other peoples have one - the moon, five - a hand, etc.
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Operations on numbers People learned to add and subtract a long time ago. When several groups of root gatherers or fishermen put their catch in one place, they carried out the addition operation. People became familiar with the operation of multiplication when they began to sow grain and saw that the harvest was several times greater than the amount of grain sown. And when animal meat or nuts were divided equally, the division operation was used.
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Ancient Greece In the middle of the 5th century. BC e. Alphabetical numbering appeared in Asia Minor. Numbers were designated using letters of the alphabet, under which dashes were placed. The first nine letters denoted the numbers from 1 to 9, the next nine - 10, 20... 90 and another nine - the numbers 100, 200...900. This could be used to represent any number up to 999.
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Numbers in ancient Rome The Roman system also has special signs: The number 444, for example, is written like this: CDХLIV Using this system, you cannot write very large numbers.
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Sumerian cuneiform A Sumerian peasant brought a bow to a tax collector. "Sum!" - said the collector, because “sum” in Sumerian means “bow” - and drew it on a clay tablet that he held in his hand. The Sumerians painted signs of fish and birds, domestic animals and plants for many years. They were drawn with a reed stick (stylo) on a tablet made of raw clay. Later, the Sumerians agreed on what each icon would represent. They got rid of smooth lines - they simply pressed the stylus into the clay and immediately took it away. There were traces left on the clay - cuneiform.
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Egypt In Egypt - one of the most ancient numberings. The inscriptions of the Egyptians consisted of drawings - hieroglyphs. Two mathematical papyri have survived, which show how the ancient Egyptians calculated. For example, the hieroglyph for a hundred was drawn like a measuring rope, for a thousand - like a lotus flower, for 10 thousand - a raised finger, 100 thousand - like a toad, a million - like a man with raised hands.
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Nowadays, we write numbers in Arabic numerals - they were borrowed by the Slavs in the 13th century. Previously, our ancestors wrote down numbers using the letters of the Slavic alphabet - Cyrillic: buki, live, sha and others. A dash was placed above the letter - a title. The number 12, for example, was written like this: lead the letter with a title and the letter also with a title. It turned out: two by ten. Large numbers had their own names: the number 10 thousand, and then a million was called darkness, a million millions were called legion, and a legion of legions was called leodr, leodr leodr was called raven. In one manuscript there was a number greater than a raven. It was called a deck. If you write it in Arabic numerals, then after 1 there will be 49 zeros! Slavs
How did they think in ancient times? How did they count in the old days?
For thousands of years, peoples have created legends and myths, reflecting their dreams and aspirations in them. Not being able to fly like birds or run faster than a deer, people came up with fairy tales about flying carpets or running boots. Suffering from hunger, they dreamed of a self-assembled tablecloth. But most of all they wanted to make their hard work easier. This is how tales arose about Emel and his miracle stove, Aladdin’s lamp, about wonderful mechanical and magical assistants and many others.
But while poets were writing poems, and writers were writing novels, scientists were taking the first steps to create automata. Even in ancient times, machines were invented that dispensed “holy” water in churches when a coin was dropped into them. Other machines opened doors when the priest approached and performed other “miracles” that made the people tremble before the omnipotence of the gods. Greek craftsmen built quite complex mechanical toys, including a mechanical theater in which entire performances were performed. These wonderful mechanisms were rare; they were not widely used, because the bulk of the population was uneducated. However, life forced people to learn to count and understand mechanisms.
At first, people counted “in their heads”, then they began to use improvised means - bone, clay and wooden beads, even their own fingers helped people.
The most ancient counting devices did not appear immediately. At first, the need for counting was small, and people had enough of their own fingers and the fingers of their neighbors in order to count military booty, the number of hunting trophies, knives, spears, warriors, etc. In ancient times, writing was poorly developed, and every person needed to count, so they had to use their own fingers, notches on bones, pebbles, beads and other small objects to count. But when people began to cultivate the land and domesticated some animals, they needed many more items for counting and the ability to perform operations with numbers.
To successfully engage in agriculture, arithmetic knowledge was necessary. Without counting days, it was difficult to determine when to sow fields, when to start watering, when to expect offspring from animals. It was necessary to know how many sheep were in the herd, how many bags of grain were put in the barns, etc.
Several decades ago, archaeological scientists discovered a camp of ancient people. In it they found a wolf bone, on which 30 thousand years ago some ancient hunter struck fifty-five notches. It is clear that while making these notches, he was counting on his fingers. The pattern on the bone consisted of eleven groups, with five notches in each. At the same time, he separated the first five groups from the rest with a long line. The oldest artifact of this kind is the “Ishango bone”, found in the Congo (about twenty thousand years old). This is a baboon shin bone covered with serifs.
The word “tag” is still preserved in the Russian language. Now this is the name given to a tablet with a number or inscription, which is tied to sacks of goods, boxes, bales, etc. But two or three hundred years ago this word meant something completely different. This was the name given to pieces of wood on which the amount of debt or tax was marked with notches. The notched tag was split in half, after which one half remained with the debtor, and the other with the lender or tax collector. When calculating, the halves were added together, and this made it possible to determine the amount of debt or tax without disputes or complex calculations.
Ancient people invented the so-called “finger counting” - when not only numbers up to several hundred were depicted on the fingers, but even arithmetic operations were performed using the fingers (in Russian the word "five" resembles a “carpus” - part of the hand, a derivative from it - “wrist” - is often used now). The ancient Egyptians believed that in the afterlife, the soul of the deceased was tested by counting on their fingers. And in one of the ancient Greek comedies, the hero says that he prefers to calculate the taxes due on his fingers. Ancient people also learned to multiply single-digit numbers from 6 to 9 on their fingers.
In Rus', this method of counting on fingers was common: mentally number the fingers on both hands. Little finger - 6, ring finger - 7, middle finger - 8, index finger - 9, thumb - 10. Let's say you want to know how much 8 x 7 is. Put it together middle finger left hand (8) with the ring finger of the right (7). Now count. The two connected fingers plus those below them indicate the number of tens in the work. In this case - 5. Multiply the number of fingers above one of the closed fingers by the number of fingers above the other closed finger. In our case, 2 x 3 = 6. This is the number of units in the desired product. We add the tens with the ones, and the answer is ready - 56. Check the other options, and you will see that this old Russian method does not fail.
A complete description of finger counting was compiled by the Irish monk Bede the Venerable, who lived in the 7th - 8th centuries AD. He described in detail how to represent various numbers on the fingers, up to a million. In some places, finger counting has survived even today. For example, at the world's largest Chicago grain exchange, brokers on their fingers, without uttering a single word, report offers, requests, and prices for goods. And Chinese merchants bargained by holding each other's hands and indicating the price by pressing certain knuckles. Is this where the words “shake hands”, which once meant concluding a trade deal, came from?
With the advent of the first states of Ancient Egypt, Mesopotamia, China, Ancient Rome, and the states of America, it was necessary to perform calculations with very large numbers - after all, it was necessary to calculate taxes, receipts of military booty in the treasury, tribute from conquered states, and calculate the construction of roads and temples. Merchants kept records of goods, profits received, etc. In those days, there was even a government position for those who carried out calculations - a scribe. The larger the numbers and more complex the calculations, the greater the chances of confusion and mistakes. And the most complex calculations were required to be carried out first by priests, and then by scientists for astronomical calculations - the movement of the moon, stars, sun on which agriculture, harvest and the well-being of the entire state depended!
How were ancient engineers, mathematicians and astronomers able to create machines and make calculations that are considered complex even today?
Counting devices.
In ancient states, scribes - the people who carried out calculations - were entrusted with a very difficult task - they had to keep records of government revenues and expenses, and these were always very large numbers that were difficult to calculate in the mind. And here the ancient people showed amazing ingenuity - they created hand-held devices for counting:
- was one of the first abacus – it was invented in Ancient Egypt, it was also known in Babylon, then it was borrowed by the Greeks and Romans. Its device is different time and changed in different places, but the main idea behind this device was the following: it was a board with longitudinal grooves, in which pebbles were initially placed, and in later times - special tokens. As the Romans called the pebble calculus (compare with the Russian word "pebbles") , then the counting on the abacus was called calculation. And now the calculation of prices for goods is called calculation, and the person performing this calculation is calculator . On the abacus, the rightmost groove served for units, the next one for tens, etc.
- A similar counting device was used in Ancient China - suan-pan and Japan - soroban . Only the pebbles were not moved in the grooves, but the beads were moved on wires. Using Chinese suan pan you could even extract the roots!
- The ancient Mayans also used a device that looked like a small model of a fortress - yupana – where the number 40 was taken as the basis for counting, and not 10 as in Europe.
- abacus appeared in Rus' in the 16th century and were used quite effectively until the end of the 20th. They are still very convenient for the blind.
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We are all accustomed to ordinary facts - there are 24 hours in a day, a month has 30 days, and there are 365 in a year. Mechanical and Digital Watch- our everyday reality, and today it is difficult to imagine that it could be different. How did people live before modern watches were invented? What methods of calculating time do other peoples have? We will look at the answers to these questions below.
In ancient times there were various ways determine time. The sundial helped to navigate by the shadow cast by the Sun as it moved across the sky during the day. They included a pole (gnomon) that cast a shadow, and a dial with marks along which the shadow moved. The very principle of operation of the watch implies its complete dependence on the Sun, so it was impossible to use this watch at night or in cloudy weather. Different peoples of antiquity, such as Egypt, Rome, China, Greece, India, had their own types of sundials, which differed in design.
The water clock was a cylindrical vessel from which water flowed drop by drop. The time was determined by the amount of water flowing out. Such watches were common in Egypt, Babylon, and Rome. However, there was another type of water clock, which was common in Asian countries - a floating vessel was filled with water, which entered through a small hole.
We are all familiar with the hourglass. They existed before our era; in the Middle Ages their development was improved. For the accuracy of the watch, the quality of the sand and the uniformity of its flow were of great importance; it was specially made. Fine black marble powder was used, as well as pre-treated lead and zinc dust sand and other types of sand.
Time was also determined using fire. Fire clocks were very common in ancient times, especially in homes. There were different types such clocks - candle, wick, lamp. In China, where fire watches are believed to have first appeared, a common variety was common, consisting of a base made of flammable material (in the form of a spiral or stick) and metal balls attached to it. When a certain period of the base burned, the balls fell, thus beating time.
In Europe, candle clocks were popular, which made it possible to determine the time by the amount of burned wax. This variety was especially common in monasteries and churches.
We can also mention such a method of determining time in ancient times as orientation by the stars. In Ancient Egypt, there were star maps, which were used by Egyptian observers to navigate at night when using a passage instrument.
It should be noted that in ancient Egypt there was also a 12-hour division of day and night, but the hours were not of equal length. In summer, daytime hours were longer, night hours were shorter, and in winter, the opposite was true. A month according to the Egyptian calendar consisted of 30 days, the year had 3 seasons of 4 months each. For the Egyptians, the Nile served as the basis of life, and the seasons were closely related to the events around the river: the time of the river's flood (akhet), the time of the land's emergence from the water and the beginning of agriculture (peret), and the time of low water (shemu).
New Year The Egyptians celebrated in September, with the appearance of the star Sirius in the sky.
IN Ancient Rome the year consisted of only 10 months (304 days). The beginning of the year was in March. Subsequently, the Roman calendar underwent changes - Julius Caesar established a calendar year of twelve months, the beginning of which was determined to be January 1, since on this day the Roman consuls took office and a new economic cycle began. This calendar was called the Julian calendar. The names of the months that are familiar to us since childhood - January, February, March, etc. - came to us from Rome.
Nowadays, in most countries, time is counted from the Nativity of Christ and the Gregorian calendar is adopted. However, there are other options for counting time. For example, in Israel, chronology is calculated from the creation of the world, which dates back to 3761 BC. according to the tenets of Judaism. There are 3 types of year in the Jewish calendar - correct, consisting of 354 days, sufficient, numbering 355 days, and insufficient, consisting of 353 days. In a leap year, one extra month is added.
Everyone knows chinese calendar, in which each year is dedicated to a specific animal. At first, China adhered to it, but with the emergence of communism in this country there was a transition to the Gregorian calendar. Eastern calendar is still used in China today to determine the dates of holidays, such as the Spring Festival, which is Chinese New Year, and the Mid-Autumn Festival. New Year in China is a variable holiday and falls on the “First New Moon Day,” which is between January 21 and February 21.
Today, there are other examples of time systems that reflect the vision of the world and the traditions of the peoples who created them.