Project of units of measurement in different countries. Units of measurement of different countries. Equipment and materials

Units of measurement of different countries. Each country in the world uses its own methods of measuring volume, weight and quantity, that is, it has a special system of measures. It is important to successfully conduct trade and exchange of goods. But the most difficult thing is that in different countries these systems of measures do not coincide. For example, the United States borrowed a special, “English” system of measures from the British. Today the US is practically the only country that uses it.

Mathematics 2nd grade

“Actions on numbers” - Multiplication and division Multiple comparison of numbers. Literal expressions. 2nd grade. Arithmetic operations (65 hours). Division. Addition table. Identification and comparison of special cases of addition and subtraction of two-digit numbers. Using multiplication tables to perform division table cases.

“Commutative property of multiplication” - Organizational moment. Updating knowledge. Commutative property of multiplication. Consolidation of what has been learned. Lesson plan. Working on new material. Bottom line. Verbal counting. Primary consolidation. Setting learning objectives.

“Actions with numbers” - Consolidation. X+14=21 35 7 9. New material. 5 8=40. Mathematics 2nd grade. Magic house. Increase 8 by 17 Decrease 33 by 8 Find the sum and difference of the numbers 16 and 5 Which number is greater than 9 by 7? Verbal counting. “X” is a reference to the mathematical pole. Replace addition where possible with multiplication. 3+3+3+3+3+3+3= 4+2+1+4= 7-7-7-7= 4+4+4+4+4=. Purpose: to introduce a new action, to reveal the meaning of the action of multiplication. Topic: Multiplication.

“Peterson mathematics 2nd grade” - 8. P. 26. 38 + 19. 5. 4. 1m. Vision! Lesson topic: 10. 22. Well done! Meter. 3 m. 10 dm. IN. ? 3 dm less. "Meter". Ancient units of measurement: 30 - 16. Find the perimeter of the rectangle: D. 1. It's time to rest! 3. A. 11. 100 cm. =. 50. 57. Mathematics L. G. Peterson, 2nd grade. A. 14. 13. 8 m. 8 dm. Take care. 45 – 23.

"Meter" - Centimeter. Math lesson in 2nd grade on the topic “Meter”. What can you measure with a meter? 100 cm. Decimeter. Meter. 10 dm. Practical work. Ancient units of measurement: Express in decimeters:

"Measurements" - Meter. 2. The metric system was adopted in France at the end of the 18th century. Student 2 "A" class FIRSYANKOV NIKITA. But constantly traveling to Paris to check the standard meter is very inconvenient. Units of measurement of different countries. The length of a foot is 30.48 cm. Standard. "Units". Metric system. How did units of measurement appear?

Project language:

Study

Target

Study the history of numbers;

Compare the records of numbers of different nations.

Hypothesis

Different nations wrote numbers differently.

Equipment and materials

Basic research methods:

literature analysis, comparison, student survey, analysis and synthesis of data obtained during the study.

LITERATURE

Illustrated encyclopedic dictionary. Moscow. Scientific publishing house

"Great Russian Encyclopedia", 1998.

“Entertaining arithmetic” Perelman Ya.I. Moscow, Triada-Litera, 1994.

AND I. Depman, History of Arithmetic, 1965

“For schoolchildren about mathematics and mathematicians.” Compiled by Liman M.M. Moscow,

Education. 1989 "

"I'm exploring the world." Children's encyclopedia. Moscow, “Astrel”, 2004.

Kuzmishchev V.A. The secret of the Mayan priests. 2nd ed. -- M., “Young Guard”, 1975

All kinds of numbering and number systems (http://www.megalink.ru/~agb/n/numerat.htm)

Study protocol

CHAPTER 1.

What is a number?

Everything we don’t think about seems simple to us. Here, for example, are the numbers.

Math can still be complex, and numbers are simply icons that represent the numbers zero through nine. It seems to us that it cannot be any other way! But many civilizations thought differently.

Numbers have always been there 4 and 5 thousand years ago, only the rules of representation

theirs were different. But the meaning was the same: the numbers were depicted using

certain signs - numbers. A number is a symbol involved in writing a number.

A number is a quantity that is made up of numbers according to certain rules.

These rules are called number systems.

Before the advent of numerical designations - the numbers and letters with which we now associate numbers, our early ancestors used “standards”, which they chose according to the associative principle. For example, everyone knew that there was only one moon in the sky, a person had two hands (or eyes), and five fingers on each hand. Poetic echoes of such a system can now be found in the early verbal counting of the Hindus, where the unit was called the Earth, the Moon, Brahma; two - “twins”, “eyes”; five - “feelings” and so on.

Later, the ancients finally decided that it was necessary to count by what is in abundance and what is always with you, and they chose fingers, so the vast majority of number systems are based on the principle of counting in tens (by the number of fingers on both hands). Of the currently existing exceptions to this rule, we can recall the French language, where counting is done in twenties: 80 - quatre-vingts (4*20), 90 - quatre-vingt-dix (4*20+10). But here again, twenty is the total number of fingers and toes.

Throughout the centuries-old history of mankind, there has been

many different ways of writing numbers, some have survived to this day,

and some remained in history.

Several decades ago, archaeological scientists discovered a camp

ancient people. They found a wolf bone on it, on which 30 thousand years ago

ago, some hunter made 55 notches. It is clear that, while making these notches, he

counted on his fingers. The pattern on the bone consisted of 11 groups, with 5 notches in each. At

In this case, he separated the first 5 groups from the rest with a long line. Later in Siberia

and other areas, (stone) shipwrecks made in that distant era of the Stone Age were found, on which there were also lines and dots, grouped in 3, 5, or 7.

CHAPTER 2.

Figures of ancient civilizations

Numbers in Ancient Egypt

The first written figures for which we have reliable evidence are

appeared in Egypt and Mesopotamia about 5,000 years ago. Although these two cultures

were far from one another, their number systems are very similar:

using notches on wood or stone to record days gone by.

Egyptian priests wrote on papyrus made from the stems of certain

varieties of reed, and in Mesopotamia on soft clay.

In the Egyptian system, numbers were hieroglyphic symbols;

A unit was denoted by the same hieroglyph as a line, a ten by a heel, a hundred by a loop of rope, a thousand by a lotus. But ten thousand is especially unexpected for a European, because it is this part of the body that we associate with pitiful units - the finger! One hundred thousand was represented by a toad, but the million sign was unique. It depicted a man kneeling and raising his hands, as if in shock at such a number. Although, if you think about it, a million is just a hundred toads or a thousand fingers.

Numbers not divisible by 10 were written by repeating these numbers. Each

the figure could be repeated from one to 9 times.

Mayan numbers

But the Mayans had two ways to write numbers. Probably for boring people and for fun ones. In the boring system, zero was written with a shell, one with a dot, five with a line, and these three symbols were enough to indicate any number. Moreover, numbers were written on approximately the same principle as ours, only the system was not decimal, but 20. That is, the notation dot and shell (10) meant our twenty (20). And ten was written as two lines (5 and 5).

The second way to write numbers is with hieroglyphs in the form of heads, each of which represents a number.

from 0 to 19. Moreover, this system was half decimal: starting from 11, the head has a clear added jaw, like 10.

Obviously, the first type of notation was used for calculations, as it was more visual, and head figures were only used for calligraphy on stone. Such figures were used extremely rarely, surviving only on a few monumental steles.

Incas numerals

The Incas had two types of writing. Classical, in knots (“kipu”) and two-dimensional, in the form of notes on parchment, leaves and even ornaments on clothes (“sprat”). The quipu had several types of complexity. All adult Incas knew numerical notation using knots.

Simple writing was used by educated people (for example, officials - the Incas were a very bureaucratic empire), and complex writing, necessary for detailed and detailed records, was used only by scientists and chroniclers. By default, sprat was considered an elite type of writing; ordinary people were forbidden to use it. Numbers, like words, were denoted by knots of a certain shape. Scientists claim that the Incas used a decimal number system and wrote down numbers as we show them on an abacus - only instead of rows of dominoes there were rows of knots.

During the Spanish and Portuguese colonization of South America, the Spaniards systematically destroyed quipus. Thus, many priceless historical chronicles disappeared. The Incas were the first people to use double counting in accounting (recording debits and credits). For calculations they used a specific type of account, yupana. Some modern scientists believe that Yupana worked on the Fibonacci number system, invented by the Incas, long before Fibonacci.

Babylonian cuneiform

The Babylonians used a sexagesimal number system, but within each sixty, judging by the way it was written, it was an ordinary decimal number system.

The Babylonians were famous for their astronomical observations and calculations (using their invention of the abacus). They inherited this number system from the Sumerian and Akkadian civilizations. It was used two thousand years BC. e.

Only two signs were used to write numbers: a straight wedge to indicate units and a lying wedge to indicate tens within the sexagesimal digit. A new sexagesimal digit began with the appearance of a straight wedge after a recumbent wedge, if we consider the number from right to left.

The Babylonians used zero, although they did not consider it as a separate number:

In the beginning there was no zero. Later, a designation was introduced for missing sexagesimal digits, which corresponds to the appearance of a zero

Ancient Greece figures

In Ancient Greece there were two main number systems -

Attic (or Herodian) and Ionic (also Alexandrian or alphabetic).

The Attic number system is a non-positional number system used in ancient Greece until the 3rd century BC. e. She uses Greek letters as numbers, and the numbers were the first letters of the words that denoted the corresponding numbers.

The line denoting a unit, repeated the required number of times, meant numbers up to four.

After four lines, the Greeks introduced a new symbol instead of five lines Π , the first letter of the word "penta" (five). When they reached ten, they introduced another new symbol Δ , the first letter of the word "deca" (ten).

Since the system was decimal, the Greeks needed new symbols for each new power of the number 10: the symbol H was 100 (hekaton), X - 1000 (hilio), the symbol M - 10000 (myrio or myriad). The numbers 6, 7, 8, 9 were designated by combinations of these signs.

When writing numbers, the larger numbers were written down first, then the smaller ones. For example,

ΗΔΔΠΙΙΙ - 128

MMΠΔΔΔΔ - 25,040

The principle of recording numbers in the Attic number system has significant similarities with the Roman system. This may be due to the influence of Eastern Mediterranean cultures on the Etruscans, from whom the Romans borrowed the number system.

Ionian or Modern Greek - non-positional notation .

Ancient Chinese figures

This numbering is one of the oldest and most progressive.

It originated about 4,000 thousand years ago in China.

Although Chinese numbers are gradually being replaced by Arabic numerals in everyday use, they nevertheless continue to be widely used.

There are two sets of characters - regular notation for everyday use and formal record, used in a financial context

Numbers were recorded starting with large values ​​and ending

smaller. If there were no tens, ones, or some other digit, then

At first they didn’t put anything in and moved on to the next category. (In time

Ming dynasty, a sign was introduced for the empty digit - a circle - analogous to ours

zero).In order not to confuse the digits, we used several service

hieroglyphs written after the main hieroglyph, and showing what

the hieroglyph-digit in this digit takes on the meaning.

Slavic Cyrillic numbering

This form of writing numbers was completely similar to the Greek writing of numbers. If you look carefully, you will see that after “a” comes the letter “c”, and not “b” as it should in the Slavic alphabet, that is, only letters that are in the Greek alphabet are used.

To distinguish letters and numbers, a special icon was placed above the numbers - title (~)

Roman numbering

Roman numerals appeared 500 BC among the Etruscans, who may have borrowed some of the numerals from the proto-Celts.

The ancient Roman number system was based on the use of letters to represent numbers. Each letter had a different meaning, each number corresponding to the position number of the letter

Time flies. Time is flowing. It is money, it endures or not, it exists or not, it is also the fourth dimension in Minkowski space, one of the many rational projections of the little-knowable Universe. And this dimension is given a huge number of properties, real and fictitious.

Meanwhile, nowadays, in different countries of the world, calendars and alphabets, units of distance and mass may be different, but seconds, minutes and hours are accepted everywhere. Although no one is stopping you from highlighting your originality and acting like cashiers and salespeople who “will be with you in 5 minutes.” stretches out to several hours (and everyone remains alive).

Why did it happen so? Moreover, some people live clearly slower than others. Perhaps because those who wanted to live on Earth always had to “be able to spin” at different speeds - just as the planet itself can. From its revolutions around itself, days are formed, more precisely, days, around the Sun - years. In Nepal it is now 2071, in Ethiopia it is 2006.

History and various sciences have preserved for us several alternative measures for time. For example, the word “moment” is known. But when it is used out loud, it is rarely meant that the interlocutor or client should wait exactly one and a half minutes. That is, the unit of time “moment” is historically equal to 90 seconds - one fortieth of an hour. This is how it was customary to split eternity and put divisions on dials in the Middle Ages. I wonder if the Russian equivalent of “moment” - the word “minute” - can be equated to 60 or another number of seconds?

All over the world, electronic and mechanical, they are configured according to the so-called. atomic clocks, the evolution of which, like computers, has already reached pocket size. Our current list of units of the “fourth dimension” will begin with the atom.

Atom

“Tom” means “to cut”, “to divide”, “atom” means “indivisible”, as the ancient Greeks established in their time. Until some time, an atom was considered the smallest particle of matter. And in the old English language (Anglisc) an “atom” was called something like an instant. That is, the shortest amount of time that can be measured.

In this sense of the word, 1 “indivisible” atom is equal to 1/376 of a minute. This is 0.15957 seconds. With the advent of cinema and modern physics, the need for such a unit of time obviously disappeared.

Gary

The Indian word "ghurry" is similar to the culinary term "curry", and also differs in its pungent approach to the issue. In the Middle Ages, Indians “switched bodies” between hours and minutes, as if there were 60 hours of 24 minutes each in a day.

The Gary water clock was a brilliant invention in its simplicity and accuracy. Take a wooden or metal cauldron of a certain size with holes determined by its design. Such an empty container is immersed in a pool or trough with water, liquid begins to flow into the vessel through the holes, and in the end the water-filled container sinks, sinking to the bottom of the pool. Typically, 24-minute basins were used, so a day was equal to 60 gari.

Chandelier

The word “lustr” refers to a period of time equal to five years. The fashionable word “lustration” in Ancient Rome meant a cleansing sacrifice of animals on the Campus Martius after the next census of the empire’s population. They were given over to the ceremonial fire, and this supposedly protected all civilians registered by Rome from the wrath of the gods. Such fiery censuses in the Eternal City and its possessions have been carried out since 566 BC.

The last rite of fire lustration was performed by Vespasian in the year 74, then Caesar the reformer abolished the custom. Nowadays, if the procedure of the same name is performed, it is without murder, and the word “luster” to denote a period of time has forever been replaced by the “five-year plan.”

mile

Just as a light year is a measure not of the calendar, but of distance, so distance can be a measure of time. For example, land mile. Namely - mileway. In the Middle Ages, this term was sometimes used to refer to the time it would take an average pedestrian to cover a distance of one mile. Without an exact value, the time mile was usually converted to approximately 20 minutes.

Nundins

In Ancient Rome, nundines (from the words “novem dies” - 9th day) were called market days on which peasants came to cities to sell agricultural products. Many residents of the outskirts lived only from Nundina to another, and there was an 8-day break between market dates. Therefore, the periods of time from trade to trade themselves began to be called nundins in everyday life.

Kenzem

In French, the word "quinzième" literally means "fifteenth". After the Norman conquest of England, “kenzem” was borrowed by the newborn English language, and this term was used to refer to the 15-penny tax that was levied on every pound in the monarchy.

At the beginning of the fifteenth century, the word "kenzem" began to be used in a religious context. Meaning the day of some Christian holiday and the following two post-holiday weeks. That is, it turned out to be a 15-day period.

Scruple

The word comes from the Latin "scrupulus", which means "small pebble" or "pebble". Historically, scruple was a term from the professional language of pharmacists. A scruple was equal to 1/24 of an ounce, i.e. approximately 1.3 grams. In Russian they would say “pinch”.

In the figurative sense of “a small amount of something,” the word “scruple” began to be used as a name for a measure of time in the early 17th century. They began to call the distance from division to division on a 60-digit dial, i.e. 1/60th of a circle. It could be a minute (and 60 minutes are equal to an hour), or a second (1/60 of a minute), or 24 minutes (the sixtieth part of a day). Let us recall that the medieval inhabitants of India measured their times with the last measure.

Particular attention should be paid to the question of the medieval system area measures, since in the era of feudalism it was the measurement of land plots that was the most pressing matter.

In the early Middle Ages, a new unit of area appeared - bonus. Its exact meaning is still unknown. It may have been 1.28 hectares

From the very beginning of the Middle Ages, there was a practice of measuring land by measures of the grain that could be sown on it. Sometimes this measurement was carried out descriptively: “a field where two modia of grain can be sown”). There were also other ways to measure land: by the crop that can be harvested here, by the number of livestock that can be grazed here, by the length of the perimeter of the plot.

And yet, starting from the early Middle Ages, attempts were made to unify weights and measures.

More or less clear systems of area measurements were formed in England and Germany during the High Middle Ages. In medieval England, the original unit of land ownership, as well as the fiscal unit, was guide(from the English “household, members of the household”). Gaida originally meant a land area sufficient to feed a peasant family for a year. The guide was divided by 2, 3, more often - by 4 virgates, and virgata, in turn, by 2 or 4 Farthingdale. A more or less accurate idea of ​​the area of ​​a gaida can be obtained starting from the 11th century, when it and related units began to be counted in acres. Acre was the second “basic standard” unit and was originally understood as the area of ​​\u200b\u200ba piece of land that a team of oxen could plow in a day.

The number of acres in the guide could be 60 (about 24.3 hectares),

A larger unit of area in England than the acre was mile², equal to 640 acres (2.59 km²). The acre itself consisted of 4 ores. In one ore – 40 childbirth². 1 genus² consisted of 30.25 yards². 1 yard² equaled 9 ft². 1 ft² consisted of 144 inches

In Germany, the “analog” of the guide was Gufa. It looked like an English acre morgen.

Gufa becomes a unit of area from 7 to 12 hectares.

Note that the word “morgen” denoted the area of ​​the field that could be plowed in the first half of the day, hence the name, which translates as “morning.” Morgens, in turn, were divided into sections rue. Rute, like virgata, also means measuring pole, rod. There were 120, 160, 180, 240, 300, 400 of them in various morgens.

In some regions of Germany, such a unit of area was used as ioh from 30 to 55 ares (acres). Another old German area measure was tageverk(from the German “one day’s work”), which was equal to 0.23 - 0.36 hectares.

The most famous system measures of length developed in the medieval England. It acquired its finished form under Elizabeth I:

Inch– means “thumb” in Dutch. It was originally an inch long and was defined as the length of the joint (last phalanx) of the thumb of a man's hand.

In the metric system, an inch is 2.54 cm.

Hand– means “hand” in English. It is equal to four inches, i.e. 10.16 cm. The measure was used primarily to measure the height of horses.

Foot– means “foot” in English. During the period of historically the first attempts to introduce legal units, the foot was defined as “the average length of the steps of 16 people leaving Matins on Sunday.”

Yard– in Old English means “stick, branch.” It is equal to three feet. According to legend, a yard, by decree of King Henry I, issued in 1100, was defined as the distance from the middle of his nose to the end of the middle finger of his outstretched hand.

mile– translated from Latin means “a thousand double steps.” In England it was equal to 8 furlongs, i.e. 1609.344 m.

Another well-known system of length measures was French (more precisely, Parisian), based on a unit called Toise and similar in origin to the Russian oblique fathom. A toise was approximately 1.9 m, so when the French speak of a tall man as “long as a toise,” their comparison is much less of an exaggeration than, say, a similar Russian proverb “as long as the Kolomna verst.” Long distances in France were measured miles And leagues. Lie, in accordance with Gallo-Roman traditions, was equated to 1.5 miles (which was approximately 4.8 km).

Typical for Germanic lands the system of relationships between the basic units of length is formulated in treatises on field markings. According to these works, four fingers make a palm, four palms make a foot, and two feet make a cubit. Long distances in the German lands were measured in miles. The great German mile was close to 7.3 km in length, but this is only one of many miles used in Germany. The German nautical mile used in the Baltic was approximately 10 km.

Initially, in France, and throughout cultural Europe, they used Latin measures of weight and length. But feudal fragmentation made its own adjustments. Let's say another senior had the fantasy of slightly increasing the pound. None of his subjects would object; they shouldn’t rebel over such trifles. But if you count, in general, all the quit grain, then what a benefit! The same goes for urban artisan workshops. For some it was beneficial to reduce the fathom, for others to increase it. Depending on whether they sell or buy cloth. And now you have the Rhine pound, and the Amsterdam pound, and the Nuremberg and Parisian pound, etc. More than a dozen different units of length rotated in the south of France alone.

True, in the glorious city of Paris, in the fortress of Le Grand Chatel, since the time of Julius Caesar, a standard of length has been built into the fortress wall. It was an iron curved compass, the legs of which ended in two protrusions with parallel edges, between which all the fathoms in use must fit exactly. The Chatel fathom remained the official measure of length until 1776.

The metrological reform of Peter I allowed English measures to be used in Russia, which became especially widespread in the navy and shipbuilding - yards, feet, inches .

Yard was defined as the distance from the nose of King Henry I of England to the tip of the middle finger of his outstretched hand. This yard, equal to 0.9144 m, is still used in England. The yard was divided into 2, 4, 8 and 16 parts, called respectively half yard , span , finger And nail .

Yard = 91.44 cm

Foot was defined as one third of a yard. A foot is the average length of a person's foot (the English word "foot" is foot). On one Sunday in 1324, another king, Edward II, ordered that 1 foot be determined as the arithmetic mean of “the length of the feet of 16 people.” 16 Englishmen lined up in a chain in such a way that each next one touched the heels of the previous one with the ends of his toes. One sixteenth of such a chain was one foot. Since then:

1 ft = 30.48 cm, A 1 yard = 3 feet = 91.44 cm.

Lee– Chinese unit of distance measurement. In ancient times it was 300 or 360 steps, the modern generally accepted value is 500 meters.

Stages- a unit of measurement of distances in the ancient systems of measures of many peoples, introduced for the first time in Babylon, and then passed on to the Greeks and received its Greek name. It is not specific enough for us. In most systems of measurement this distance was equal to 600 feet. The Greek stade is equal to the distance of 600 feet of Hercules. According to legend, this is how many steps Hercules managed to take from the moment the first rays of the sun appeared over the Krona Hill in Olympia until the sun rose above the earth. There are different values ​​of the stage: Babylonian = 194 m; Greek = 178 m; Attic = 177.6 m; Olympic = 192.27 m; Egyptian = 172.5 m; stages of the pharaonic system = 209.4 m; Roman = 185 m; stages of the Persian system = 230.4 m.

Traditional Japanese measures of length are still used in some industries in Japan, despite the fact that Japan has long had a metric system.

A wide variety of length measures were used throughout. And only the transition to the metric system of measures put an end to this confusion.