When did people learn to swim? Research work "how people learned to count".

Research work

1. Introduction

2. Main body

2.1. How did the account come about?

2.2. Writing numbers for different peoples

2.3. counting devices.

3. Conclusion

4. Literature.

Introduction

I chose the topic "How people learned to count" because I was interested in who and how first came up with numbers, numbers and counting. I was also interested in the account entries in different countries.

Targetmy work: to understand how people learned to count.

. To achieve my goal, I set myself such tasks:

· To study the history of the emergence of numbers, numbers and counting.

· Learn how to register an account in different countries.

Objectsmy research are: numbers and numbers.

Productresearch is: presentation and abstract.

Main part

Ancient people obtained their food mainly by hunting. The whole tribe had to hunt for a large animal - a bison or an elk: you cannot cope with it alone. The leader of the raid was usually the oldest and most experienced hunter. So that the prey did not leave, it had to be surrounded, well, at least like this: five people on the right, seven behind, four on the left. Here you can't do without an account! And the leader of the primitive tribe coped with this task. Even in those days when a person did not know such words as "five" or "seven", he could show the numbers on his fingers.

There are even now on earth tribes that, when counting, cannot do without the help of their fingers. Instead of the number five, they say "hand", ten - "two hands", and twenty - "the whole person", - here the toes are counted.

Many, many years passed. A person's life has changed. People tamed animals, and the first cattle breeders appeared on the earth, and then farmers.

The knowledge of people gradually grew, and the further, the more the need for the ability to count and measure increased. Cattle breeders had to count their herds, and at the same time, the number could go up to hundreds and thousands. The farmer needed to know how much land to sow in order to feed himself until the next harvest. What about sowing time? After all, if you sow at the wrong time, you will not get a harvest!

The calculation of time by lunar months was no longer suitable. needed more accurate calendar. In addition, people increasingly had to deal with large numbers that are difficult or even impossible to remember. I had to figure out how to write them down. The first way to "write" numbers- notches on animal bones, knots on ropes, a pebbles or other objects were used for counting.

About five thousand years ago, almost simultaneously in different countries - Babylonia, Egypt, China - was born new way number entries. People came up with the idea that numbers can be written not just in notches-units, but in digits: hundreds separately. This was a very important discovery. Counting and writing numbers is now much easier.

The ancient Egyptians, just like we do now, counted in tens. But they had special digits only for digits: units, tens, hundreds, thousands.

In ancient Babylon, they counted not in tens, but in sixties. A mathematician would say that the counting system there was not decimal, like ours, but sexagesimal. The number sixty played with them the same role as ten with us.

The Babylonians used only two numbers. A vertical line denoted one unit, and an angle of two recumbent lines denoted ten. They got these lines in the form of wedges, because the Babylonians wrote with a sharp stick on damp clay tablets, which were then dried and fired.

The Chinese, like the Egyptians, used the decimal system. Here are the Chinese characters - numbers:

The hieroglyphs for writing numbers were too inconvenient, too many different hieroglyphs would have to be memorized. For further improvement counting arts one of two things was needed - or move on to a more convenient letter, i.e. move from hieroglyphs to letters, or invent some new trick, which makes it easier to write numbers with special characters. Some nations took the first path, others - the second.

The early development of written counting was hampered by the complexity of arithmetic operations with the multiplication of numbers that existed at that time. In addition, few people knew how to write and there was no educational material for writing - parchment began to be produced around the 2nd century BC, papyrus was too expensive, and clay tablets were inconvenient to use. These circumstances explain the appearance of a special calculating device - abacus.

By the 5th century BC. The abacus was widely used in Egypt, Greece, and Rome. It was a board with grooves, in which, according to the positional principle, some objects were placed - pebbles, bones.

Ancient Greek abacus (board or " salami board" named after the island of Salamis in the Aegean) was a plank sprinkled with sea sand. There were grooves in the sand, on which numbers were marked with pebbles. One groove corresponded to ones, another to tens, and so on. If more than 10 pebbles were accumulated in a groove during counting, they were removed and one pebble was added in the next category.

Chinese abacus suan pan consisted of a wooden frame divided into upper and lower sections. Sticks correspond to columns, and beads correspond to numbers. For the Chinese, the basis of the account was not a dozen, but a five.

In Russia, for a long time, they counted by bones, laid out in piles. Approximately from the 15th century, it became widespread "board count" , which almost did not differ from ordinary accounts and was a frame with reinforced horizontal ropes, on which drilled plum or cherry pits were strung.

Guest article.

According to legend, Prometheus gave fire to people, for which he suffered severe punishment. Scientists tend to think otherwise. Anthropologists have established that man has obtained and learned to use fire himself.

Nutritional hypothesis of human evolution

The first evidence of the taming of the elements - fires, charred remains of animal bones, ashes, etc. - were discovered by archaeologists in Kenya. These traces were left by ancient people who lived about 1.5 million years ago. Controlled use fire is considered one of the key factors in human evolution.

For example, Harvard University professor Richard Wrangham hypothesized that the brain primitive people developed through the heat treatment of food. The assimilation of food cooked on fire required less energy. Its surplus, the professor believes, went to the formation of intellect.

Initially, primitive people mined flame after forest fires. They tried to keep it as long as possible. Ancient people learned to kindle fires on their own much later.

Taming the elements

The results of recent research indicate that primitive people began to regularly breed hearths about 350 thousand years ago. This is entirely consistent with the general paleoclimatic and cultural criteria. Anthropologists came to this conclusion based on the study of a series of ancient artifacts. The objects were discovered in the Tabun Cave, which is located on Israeli territory near Haifa. Their age is about 500 thousand years.

According to Ron Schimelmitz, Ph.D., from the University of Haifa, who led the study, the uniqueness of Tabun Cave is that an entire era of human history is described here. The discovered objects make it possible to trace the process of taming the elements step by step.

Making your own fire

The found artifacts are mainly represented by flint tools for skinning animals and chipped chips. To establish when a person learned to make fire, scientists studied about 100 layers of sedimentary deposits. Layers older than 350 thousand years did not have burnt traces. But in younger deposits, evidence of burnt flint was clearly present in the form of red and black colors.

According to scientists, the outbreak of fire among stone walls unlikely. Obviously, by this time they had already learned how to use the hearth. But the question remains not completely clear: did a person produce fire himself or simply save it?

The information obtained is quite consistent with the results of surveys carried out in neighboring territories. These data indicate that primitive people mastered the cultivation of foci throughout the Mediterranean about 350 thousand years ago. A long study of the process of taming the elements shows that a person has been learning the art of kindling fires for a very long time.

Scientific controversy

According to Schimelmitz, whose research was featured in an article in the Journal of Human Evolution, scientists know of earlier examples of the use of fire. But they are fragmentary, random. It follows that before the period established by the doctor's group, a person did not use fires constantly. In other words, the elements were beyond his control.

But some of the scientists who did not participate in the study of the Tabun cave expressed disagreement about the fresh ideas. Many of them believe that people, not yet possessing speech and writing, have mastered complex process cooking about two million years ago. These anthropologists believe that during the same period, evolution led to a change in the intestines of people, their teeth became small, and their brains increased.

But no matter what the disputes are among scientists, the development of fire is considered one of the most significant achievements of mankind.

During the primitive system, many centuries and millennia ago, our ancestors lived in tribes. They got their food in the forests, lakes and steppes. Their life was not much like the modern one. Ancient people differed from animals only in that they had the rudiments of speech, and they knew how to use the simplest tools of labor and hunting. The first people, like small children, did not know how to count. Today, a child is taught to count by his mother, father or brother and sister, but there was no one to teach primitive people, so the process of teaching humanity to count was so long, and before a person learned to count, he went through such a colossal path of learning that he could imagine such a long period pretty hard.

Ancient people, observing the nature around them, on which their life and prosperity depended, from a wide variety of objects and things, initially learned to single out only individual items. From a herd of animals - one animal, from a school of fish - one fish. Initially, they were able to define this relationship as "one" and "many".

primeval times

Frequent observations of objects consisting of many things could lead a person to ideas about numbers, or more precisely, about numbers. Our ancient ancestors, when they saw a pair of deer, they compared them to a pair of their own eyes. But when a herd of animals was shown in front of them, they said "a lot." Only after a long time of observation and dexterity, a person was able to distinguish three objects, then four, well, and then more.

The ability to count played a big role in the survival of not only one person, but of his entire tribe. So, for example, the leader of the tribe during the hunt had to correctly place people in a trap, for this he showed the number on the fingers of his hand. And later, even the toes came into play. For example, when a person needed to exchange a spear for five animal skins, he put his hand on the ground and showed that a skin should be placed opposite each finger. And if there were not enough fingers on the hands, the legs usually went into action.

Before a person learned to count in his mind, our ancestors used for this both limbs and objects of the surrounding space, a variety of sticks and pebbles. There was also a counting technique in which large numbers were obtained by adding smaller ones, for example, to name the number 4, a person represented two numbers 2.

In some nations, the system of this calculation has been preserved to this day. In one Australian tribe, counting is done in this way: the number 1 is enea, 2 is patcheval, 3 is patcheval-enea, 4 is patcheval-patcheval. Some peoples simply associated the names of numbers with objects of nature, for example, the moon meant "1", the wings meant "2", the hand meant the number "5".

written account

The evolution of man, and his need for keeping score big numbers gave impetus to the emergence of a written account. Since paper was not yet made and did not know how to do it, the calculations were carried out by means of notches on animal bones and sticks, or knots on ropes, or letters on clay tablets.

Also, having started writing on boards, various wooden tiles, a person began to master writing, and at the same time, as people learned to count, came new problem how to distinguish written characters from digital ones? To do this, some nationalities drew dashes or wavy lines over the numbers.

Another problem was the lack of the number zero. Previously, to write down the number 209, people left a space in the middle, that is, 2 9, but in this account it was very easy to get confused, and so they began to add a small dot in place of the space, which then soon turned into a modern zero.

But years passed and the number systems changed and improved, and the first who introduced modern system reckoning, turned out to be Indians. Around the 8th century, the Arabs from India brought with them examples of calculations, in their opinion, which were the easiest to use, since the derivatives were always at hand - our fingers. Europeans appreciated this system, calling it Arabic, and since then, the whole world has been using it.

I hope now that you have learned how people learned to count, and our article was interesting to you. Count right!

Biblical view

The Old Testament story says that man was created intelligent and with the God-given ability to speak. God brought animals to man "to see what he would call them, and to know what he would call every living soul."

But the first word spoken by Adam, according to Dante Alighieri, was the Hebrew word "El" - God. From Adam, Eve and their children spoke Hebrew: this language remained the only one until the “Babylonian pandemonium”.

Imitating nature

The 18th-century German historian Johann Gottfried Herder seriously shook the “divine theory” of the origin of language, which at that time was believed by the majority. The scientist argued that speech began to form at the moment when a person began to imitate the sounds of animals.

Herder's theory was ridiculed by contemporaries, calling it the "av-av thesis".

Linguist Alexander Verzhbovsky returned to Herder's hypothesis, putting forward his theory of "two-consonant first signals of onomatopoeic origin." According to the scientist, to convey the sounds of the frightening forces of nature, for example, thunder, our ancestors used the sound combinations “Gan” and “Ran”, and the signals “Al” or “Ar” were shouted when they drove the beast into a trapping pit.

The origins of the rudiments of speech, according to Verzhbovsky, should be sought in one or more habitats of the "humanized primate", from where speech was carried to all corners of the Earth. This "humanized primate", according to Verzhbovsky, was a Cro-Magnon man who inhabited Europe 40 thousand years ago.

"Brock's Center"

Homo habilis, who supposedly lived 2.5 million years ago, is often called the first representative of the genus Homo. He possessed a number of features that distinguish him from the animal kingdom: this is not only the ability to make tools and primitive clothing, but also the structure of the brain.

According to anthropologist Stanislav Drobyshevsky, the brain of Homo habilis is characterized by an increase in the development of areas that are responsible for speech.

In particular, a noticeable bulge inside the thin-walled skull indicates that it has a "Broca's center": it is he who provides the motor organization of speech and control of the brain regions that coordinate the speech apparatus.

Specialists-physiologists have restored the morphology of the upper part of the Homo habilis speech apparatus based on traces of muscle attachment on the skull. The human ancestor probably had a massive tongue and non-touching lips: this could allow the hominid to pronounce sounds phonetically similar to our vowels "i", "a", "y" and consonants "s" and "t".

From gestures to speech

American neuroscientists, comparing the structure of the brain of humans and monkeys, in particular, chimpanzees, bonobos and gorillas, noticed a very significant similarity. It turned out that the so-called "Brodman area 44", which is located in the "Brock's center", both in humans and monkeys in the left hemisphere of the brain is larger than in the right.

In humans, this area is responsible for speech, but why do monkeys need such a developed organ?

The researchers hypothesized that "Broadman area 44" in monkeys is responsible for sign language. This suggests that human speech could have developed from the gestures that our ancestors used to communicate.

Scientists from the National Institute of Deafness and Other Communication Disorders (USA) confirmed these guesses: they found out what kind of verbal and non-verbal means human communication correspond to the same parts of the brain.

The evolution of the voice apparatus

Linguist Philip Lieberman of the University of Connecticut drew attention to the importance of the pharynx in pronouncing the vowel sounds "a", "and", "u", which form the basis of many modern languages. Combining with consonants, these vowels are able to create multiple combinations, but, most importantly, instantly link the encoded series of sounds into intelligible speech.

Together with Yale University anatomist Edmund Krelin, Lieberman decided to test the extent to which ancient man was able to pronounce the sounds mentioned.

Based on the fossils, scientists reconstructed the Neanderthal vocal apparatus and found that his larynx was noticeably higher than its position at modern man.

Then the researchers in plasticine recreated the pharyngeal, nasal and oral cavity ancient man. After taking measurements, they compared them with the size of the vocal apparatus of a modern person. Further, having put the obtained figures into an electronic computer, they determined the resonances and the range of sounds produced.

The conclusion was this: our ancestors, who lived 60 thousand years ago, could not pronounce the main vowels in rapid combinations. According to scientists, the speech of ancient people was much more primitive, while they spoke about 10 times slower than a modern person.

innate function

A prominent American linguist, Noam Chomsky, put forward a bold hypothesis. In his opinion, human speech is not the result of learning - it is a genetically built-in mechanism, like hearing or vision.

He sees confirmation of his theory in the fact that infants instantly and consciously extract information relevant to speech from the surrounding noise.

Experiments in the field of genetics make Chomsky's theory quite viable. Thus, the study of human mitochondrial DNA showed: in order to achieve modern level speech should have arisen as a result of a genetic mutation 200 thousand years ago - this, as you know, is the time of "mitochondrial Eve".

However, Cholmsky believes that the whole point is the evolutionary breakthrough of language, which occurred about 50 thousand years ago, when our ancestors left Africa. The linguist sees the reasons for the “language surge” in the emergence of more complex social institutions, creative activity, tracking natural phenomena and other factors in the development of human society.

Team work

Some experts are convinced that Homo erectus must have had some form of language, since a significant part of its activities required the exchange of thoughts. The drawings on the fossils of Torralba and Ambrona already testify to the high organization of the hunting process by primitive man.

The American writer Edmund White is sure: in order to draw up preliminary plans for hunting, name animals, tools, indicate landmarks primitive should have talked. And as intra-family and public relations expanded and vocabulary our ancestor.

White's hypothesis can be confirmed by studies of human remains from the Totavel cave (France), which are supposedly 450 thousand years old. Scientists attribute them to a group of hominids, which are an intermediate species between Pithecanthropus and Neanderthals.

With the help of a computer, experts recreated the passage of sound from the lungs to the tip of the lips of the “Totavel man”. The machine gave the result in the form of sounds "aah-aah", "chen-chen", "reu-reu". For an ancient hunter, this is a very good result.

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Completed by a student of 8 "L" class

Kazimirov Yaroslav

• The purpose of my work is to show how people learned to measure time using the devices they invented and to show what periods of time can be measured using certain hourglasses.

• 1. Search for material on a given topic.
• 2. Building a chronology of the invention of devices for measuring time.
• 3. Show the theorem using an hourglass.
• 4. Show how, with the help of mathematics, we can understand which hourglass is needed to measure any period of time.
• 5. Show the most different calendars of the world and the representation of one selected date in them.

• My work is relevant in that it helps to better understand the history of "time", makes it possible to visually demonstrate the theorem. Allows you to better navigate various systems calendars to count time.

What is time?

And what time is and what its nature is is equally unclear both from what has been handed down to us from others, and from what we had to make out earlier.

• From now on, space by itself and time by itself go into the world of shadows, and only their peculiar union retains reality.
• German Minkowski
• Perhaps we should recognize the fact that time is one of those things that cannot be defined, and simply say that it is something we know: it is what separates two successive events!
• Richard Feynman

Aristotle

Absolute, true mathematical time in itself and in its very essence, without any relation to anything external, flows evenly, and is otherwise called duration.

Isaac Newton

• Our ancestors tried to measure time many thousands of years before modern clocks appeared. The history of the development of watches - means for measuring time - is one of most interesting pages struggle of human genius for understanding and mastering the forces of nature.

• The first clock was the Sun. The higher it rose in the sky, the closer to noon, and the lower it descended to the horizon, the closer to evening, and at the beginning in every day people determined only four "hours": morning, noon, evening and night.

• The first instruments for measuring time were sundials. People have long noticed that the longest shadows from objects illuminated by the Sun are in the morning, by noon they are shortened, and by evening they are lengthening again. They also noticed that the shadows during the day change not only size, but also direction. This phenomenon was used to create the simplest sundial - the gnomon. In the morning, the shadow of the gnomon faces west, at noon in our northern hemisphere - to the north, and in the evening - to the east. The position of the shadow determines the true solar time. However, the shadow from the gnomon in such a watch describes during the day not a circle, but a more complex curve, which does not remain constant not only in different months of the year, but changes from day to day.

• Later, the hourglass was invented. They could be used at any time of the day and regardless of the weather. They were often made in the form of two funnel-shaped glass vessels placed one on top of the other. The upper one was filled with sand up to a certain level. The duration of the pouring of sand into the lower vessel served as a measure of time. Such watches were made not only from two, but also from more vessels. Hourglasses were widely used on ships - the so-called "ship flasks", which served sailors to set the time for changing watches and rest. Now hourglasses are widely used mainly in medical practice.

• More convenient and not requiring constant supervision were fire clocks, which were widely used.

• One of the fire clocks used by the miners ancient world, were an earthen vessel with so much oil that was enough for 10 hours of lamp burning. With the burning of oil in the vessel, the miner finished his work in the mine. However, the accuracy of fire clocks, regardless of their design, was very low and largely depended on the condition environment- access fresh air, wind and other factors.

• More perfect were the water clocks, which, unlike the fiery ones, did not require systematic renewal. Water clocks were known and widely used in Ancient Egypt, Judea, Babylon, China. In Greece, they were called "clepsydra" ("thieves of water").

• The first water clock was a vessel with a hole from which water flowed out over a certain period of time. So, for example, in Africa, where there was a shortage of water, the person who was in charge of its distribution (“ukil-el-ma”), letting water into the peasant’s field, simultaneously filled the vessel. After the outflow of water from the vessel, the supply of water to the peasant's field was stopped; she was allowed into the fields of another farmer.

• The most complex and interesting mechanism created in the Middle Ages was the mechanical clock. There are sources claiming that such watches first appeared in Western Europe. Yet the first mechanical clock was invented in China. In 723, the Buddhist monk and mathematician Yi Xing designed a clock mechanism, which he called "a spherical map of the sky from a bird's eye view", driven by water. Water was a source of energy, but the movement was regulated by mechanisms. In 1450, spring clocks were invented, and by the end of the 15th century. portable watches came into use, but still too large to be called pocket or manual. In Russia, tower clocks appeared in 1404 and in the 15th-16th centuries. spread throughout the country.

• Atomic clock (molecular, quantum clock) - a device for measuring time, in which natural oscillations associated with processes occurring at the level of atoms or molecules are used as a periodic process. Since 1967, the International System of Units (SI) has defined one second as 9,192,631,770 periods. electromagnetic radiation, which occurs during the transition between two hyperfine levels of the ground state of the cesium-133 atom. According to this definition, the cesium-133 atom is the standard for measurements of time and frequency. The precision of the second determines the precision of other basic units, such as the volt or meter, which contain the second in their definition.

• We have 3 and 5 minute hourglasses. How much time can we measure with them, and how much can we not? If we use only the total sanding in hours, then in this case any time interval greater than 7 can be measured. As proof of this, there is the following statement:
• Let us prove that exactly km-k-m minutes cannot be measured with the help of k-minute and m-minute clocks with coprime numbers k and m. Indeed, suppose we could do this by “running” the k-minute clock x times and the m-minute clock y times. Then km-k-m=xk + ym, or k(x+1)=m(k-1-y). y0). But k-1-y
• But can we try to show in practice that it is possible to measure both exactly km-m-k and a smaller period of time with the help of an hourglass, coprime in terms of the number of time measurements?

• It turns out that it is possible! We will show using the same 3- and 5-minute hourglasses.
• Let's run them at the same time. When the sand stops flowing in the three-minute clock, we turn over the five-minute clock, and then exactly 2 minutes remain in it. Then we will begin to measure the time, first 2 minutes remaining in the clock, and then immediately turn them over again. So we counted 7 minutes! In a similar way we will calculate smaller time intervals as well. This confirms the theorem:

• If k and m are mutually prime numbers, then for any integer n one can choose integers x and y such that xk+ym=n. What does this theorem have to do with the hourglass? The most direct. It follows from it that in the presence of k-minute and m-minute hours, and then another yk minutes with the help of m-minute hours. If one of them, for example, y, is negative, then we simultaneously start those and other clocks from which sand spilled out, and at the moment when the m-minute clock counts its (–ym) minutes (y
• Thus, the k-minute clock started after the stop will count xk-(-y)m=xk+ym=n minutes.
• Therefore, with the help of any hourglass, coprime, you can measure any period of time.

• Calendar (lat. calendarium - debt book: in Ancient Rome debtors paid interest on the day of calendars, the first days of the month) - a number system for long periods of time, based on the frequency of movement celestial bodies: Suns - in solar calendars, Moons - in lunar calendars and at the same time Suns and Moons in lunisolar calendars. Also called a calendar is a list of days of the year with a division into weeks and months and the designation of holidays and a periodical reference publication with a sequential list of days, weeks, months of a given year, as well as other information of a different nature.
• In order to show what a record of a certain date would look like in various calendar systems, I will take 12/27/2017

• Apparently for the first time moon calendar was introduced about 4000 years ago in ancient Babylon. In this calendar, the duration of the months was calculated from one new moon to another, and it was believed that they alternately contain either 29 or 30 days. Thus, the average duration of the Babylonian calendar month equals 29.5 days, while the more accurate lunar month is 29.5306 days. The Babylonian calendar year consists of 12 months, i.e. 354 days, while in fact the year contains 365.2422 days.

• To eliminate this discrepancy, the priests Ancient Babylon, who were in charge of the calendar, in every three years out of eight they added one month. This amendment significantly improves the match calendar dates with the time of the onset of the new moon, the period of flooding of rivers, etc., but still is not accurate enough, since the discrepancy by more than 1/3 of a day per year remains uncorrected.
• Date: 27 Tebet 2017

• The ancient Jews originally had a lunar calendar. In the IV century BC. they switched to a lunisolar calendar, in which the ordinary or simple year is divided into 12 months. In this case, even months consist of 29 days, and odd months - of 30, Thus, a simple year is 354 days. Seven times every 19 years, an additional thirteenth month containing 30 days is inserted, such a year is called an extended year. Every 3rd, 6th, 8th, 11th, 14th, 17th and 19th years are considered elongated.

• However, 19 solar years contain 6939 ¾ days, and 19 lunar-solar Jewish calendar years are only 6936 days. Therefore, every 19 years, the discrepancy between the calendar and the astronomical year of 3 ¾ days accumulates. Therefore, in this calendar, in those years that begin on Sunday, Wednesday and Friday, one extra day is inserted. It is easy to see that such a correction turns out to be excessive. Therefore, to further refine the calendar in certain years, another amendment is introduced, shifting the beginning of the year one day back. Thus, the Jewish lunisolar calendar has a somewhat complex system of corrections, but it agrees quite well with the solar cycle.
• Date: 9 Tevet 5778

Mayan calendar

Mayan astronomers determined the solar year to be 365.2420 days long. Which is only 0.0002 days less than the currently accepted value of the tropical year and corresponds to a discrepancy of 1 day in 5000 years. Thus, their calendar was 1200 times more accurate than the ancient Egyptian, 40 times more accurate than the Julian and 1.5 times more accurate. Gregorian calendar which we are currently using.

The counting of years in the calculation of large periods of Mayan time was carried out in the vigesimal system, i.e. periods of 20 years, for example 201 = 20; 202=400; 203 = 8000 years etc.

The ancient Maya simultaneously used several calendars with different lengths of the year: a long one, 365 days, was used in everyday life; short, 360 days, was used for religious purposes. In addition, a calendar with a 260-day year served for some rituals. They were able to do conversions from one calendar to another with good accuracy. The connection between the lunar and solar cycles(i.e. the fact that 235 lunar months are contained in 19 solar years) was also known to the ancient Maya.

Date: 2 eb 2017

• Measuring time has always been important for a person, he is always trying to find his most accurate equivalents, but each person has his own equivalents, so there are many ways to measure time and there will be even more in the future. And mathematics can help a lot in this, because it is the most exact science that exists at the moment!