Medieval measures of length and area. Measurement units of different countries Numbers and measurements of different countries and eras

Measurement units 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 essential to successfully trade and exchange goods. But the most difficult thing is that these systems of measures do not coincide in different countries. For example, the United States borrowed from the British a special, "English" system of measures. Today, the United States is practically the only country that uses it.

Slide 10 from presentation "Measurements"... The size of the archive with the presentation is 315 KB.

Mathematics grade 2

summary other presentations

"Actions on numbers" - Multiplication and division Multiple comparison of numbers. Literal expressions. Grade 2. Arithmetic operations (65 hours). Division. Addition table. Selection and comparison of special cases of addition and subtraction of two-digit numbers. Using the multiplication table to perform table division cases.

"The displacement property of multiplication" - Organizational moment. Knowledge update. The travel property of multiplication. Consolidation of what has been learned. Lesson plan. Working on new material. The bottom line. Verbal counting. Primary anchoring. Statement of educational tasks.

"Actions with numbers" - Pinning. X + 14 \u003d 21 35 7 9. New material. 5 8 \u003d 40. Mathematics grade 2. Magic house. Increase 8 by 17 Decrease 33 by 8 Find the sum and difference of numbers 16 and 5 Which number is greater than 9 by 7? Verbal counting. "X" - a pedition to the mathematical pole. Replace addition where multiplication is possible. 3 + 3 + 3 + 3 + 3 + 3 + 3 \u003d 4 + 2 + 1 + 4 \u003d 7-7-7-7 \u003d 4 + 4 + 4 + 4 + 4 \u003d. Purpose: to acquaint with the new action, to reveal the meaning of the multiplication action. Topic: Multiplication.

"Peterson Mathematics Grade 2" - 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 measure: 30 - 16. Find the perimeter of the rectangle: D. 1. It's time to rest! 3. A. 11.100 cm \u003d. 50. 57. Mathematics L. G. Peterson, 2nd grade. A. 14.13.8 m.8 dm. Take care. 45 - 23.

"Meter" - Centimeter. Mathematics lesson in grade 2 on the topic "Meter". What can be measured 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. Pupil 2 "A" class FIRSYANKOVA NIKITA. But it is very inconvenient to constantly travel to Paris to check the reference meter. Measurement units of different countries. The length of a foot is 30.48 cm. Reference. "Units". Metric system. How the units of measurement appeared.

Any dimension associated with finding numerical values physical quantities, with the help of them, the laws of the phenomena that are being investigated are determined.

Concept physical quantities, eg, forces, weights, etc., is a reflection of the objectively existing characteristics of inertness, extension, and so on inherent in material objects. These characteristics exist outside and independently of our consciousness, not depending on a person, the quality of the means and methods that are used in measurements.

Physical quantities that characterize a material object under given conditions are not created by measurements, but only determined with the help of them. Measure any quantity this means to determine its numerical ratio with any other homogeneous quantity, which is taken as a unit of measurement.

Based on this, measuring is the process of comparing a given value with some of its value, which is taken as unit of measurement.

The formula for the relationship between the quantity for which the derived unit is set and the quantities A, B, C, ... units they are installed independently, general view:

where k - numerical coefficient (in the given case k \u003d 1).

The formula for linking a derived unit with basic or other units is called formuladimensions, and exponents dimensions For convenience in the practical use of units, such concepts as multiples and sub-multiples were introduced.

Multiple unit - a unit that is an integer number of times greater than the system or off-system unit. A multiple unit is formed by multiplying the base or derived unit by 10 to the corresponding positive power.

Fractional unit - a unit that is an integer number of times less than the system or non-system unit. Fractional unit is formed by multiplying the base or derived unit by the number 10 in the corresponding negative power.

Definition of the term "unit of measure".

Unification of measurement units engaged in a science called metrology. Literally translated, this is the science of measurements.

Looking at the International Dictionary of Metrology, we find out that unit is a real scalar quantity, which is defined and accepted by convention, with which it is easy to compare any other quantity of the same kind and express their ratio using a number.

The unit of measurement can be considered as a physical quantity. However, there is a very important difference between a physical quantity and a unit of measurement: the unit of measurement has a fixed, conventionally accepted numerical value. This means that the units of measurement for the same physical quantity are possible different.

For instance, weight can have the following units: kilogram, gram, pound, pood, centner. The difference between them is clear to everyone.

The numerical value of a physical quantity is represented by the ratio of the measured value to the standard value, which is unit of measure... The number with the unit of measurement is named number.

There are basic and derived units.

Basic units set for such physical quantities that are selected as basic in a specific system of physical quantities.

Thus, the International System of Units (SI) is based on the International System of Units, in which the main quantities are seven quantities: length, mass, time, electric current, thermodynamic temperature, amount of matter and luminous intensity. This means that in SI, the basic units are the units of the quantities indicated above.

Base unit size are established by agreement within a specific system of units and are fixed either by means of standards (prototypes), or by fixing the numerical values \u200b\u200bof fundamental physical constants.

Derived units determined through the basic method of using those relationships between physical quantities that are established in the system of physical quantities.

There are a huge number of different systems of units. They differ both in the systems of quantities on which they are based and in the choice of the basic units.

Usually, the state, with the help of laws, establishes a certain system of units preferred or mandatory for use in the country. In the Russian Federation, SI units are the main ones.

Systems of units of measure.

Metric systems.

• MKGSS,

Systems of natural units of measure.

• Atomic system of units,
• Planck units,
• Geometrized system of units,
• Lorenz - Heaviside units.

Traditional systems of measures.

• Russian system of measures
• English system of measures,
• French system of measures,
• Chinese system of measures,
• Japanese system of measures,
• Already outdated (Ancient Greek, Ancient Roman, Ancient Egyptian, Ancient Babylonian, Hebrew).

Measurement units grouped by physical quantities.

• Mass units (mass),
• Temperature units (temperature),
• Distance units (distance),
• Area units (area),
• Volume units (volume),
• Units of measurement of information (information),
• Time units (time),
• Pressure units (pressure),
• Heat flow unit (heat flow).

Units of measurement in different countries Measure everything available
measurement and do not
measurable
affordable ”.
G. Galilei

The most ancient units were
subjective units
So, for example, sailors measured the path with pipes,
that is, the distance traveled by the ship for
time for the sailor to smoke his pipe.
In Spain, a similar unit was the cigar

The program of the Olympic Games of Ancient Hellas included
running to the stage. It has been established that the Greek stage is
the length of the stadium in Olympia - 192.27 m

The ancient Romans measured distances in steps
or in double steps (step with the left foot, step
right). A thousand double steps was
mile (lat. “mille” - a thousand).

In Russia for a long time as a unit
lengths used arshin. This measure arose
when trading with eastern countries (Persian,
"Arsh" - elbow)

A span was used to measure shorter lengths
- the distance between the ends apart
thumb and forefinger. Span (18 cm)
was 1/4 arshin, and 1/16 arshin
was equal to one inch (4.4 cm)

A very common unit of length was
sazhen. The first mention of her occurs in
XI century. Since 1554 fathoms are set equal to 3
arshinam (2.13 m) and it gets the name
royal (or eagle, printed) as opposed to
arbitrary - flywheel and oblique. Makhovaya
fathom - arm span - equal to about 2.5
arshins.

China

10.

The unit of length fen was originally
the length of one grain of millet
bu - a measure of length equal to a double step
The measure of zhang length was equal to the distance between
fingertips of open hands
tribute is a load that a person is able to carry
on the shoulders, equal to 60 kg

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

In the early Middle Ages, a new area unit appeared - bonoir... Its exact meaning is still unknown. Perhaps it was 1.28 hectares

From the very beginning of the Middle Ages, the practice of measuring the land with measures of grain that can be sown on it has developed. Sometimes such a measurement was carried out descriptively: "a field where two types of grain can be sown"). There were also other ways to measure the land: according to the crop that can be harvested here, according to the number of cattle that can be grazed here, along the length of the perimeter of the site.

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

More or less clear systems of area measures were formed in England and Germany during the high Middle Ages. In medieval England, the original unit of land tenure as well as the fiscal unit was guide (from English "household, household members"). Initially, the guide was understood as a land area sufficient to feed a peasant family for a year. Gaida was divided by 2, 3, more often by 4 virgats, and virgata, in turn, by 2 or 4 farthingdale... A more or less accurate idea of \u200b\u200bthe area of \u200b\u200bthe guide can be obtained starting from the 11th century, when it and the units associated with it began to be counted in acres. Acre was the second "basic standard" unit and was originally understood as the area of \u200b\u200bland that a team of bulls could plow in a day.

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

A larger unit of measure for area in England than an acre was mile²equal to 640 acres (2.59 km²). The acre itself consisted of 4 ores... In one ore - 40 childbirth². Genus 1 ² consisted of 30.25 yards²... 1 yard² was 9 ft²... 1 sq ft consisted of 144 inches

In Germany, the "analogue" 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 \u200b\u200bthe field that could be plowed in the first half of the day, hence the name, which translates as “morning”. Morgen, in turn, were divided into sections rue... Rute, like virgata, also means a measuring pole, a rod. There were 120, 160, 180, 240, 300, 400 of them in various morgen.

In some regions of Germany, such a unit of area was also used as yoh from 30 to 55 are (acres). Another old German measure of area was tagewerk (from the German "work of one day"), which was equal to 0.23 - 0.36 ha.

The most famous system measures of length developed in medieval England... She acquired a finished look under Elizabeth I:

Inch - in Dutch means “thumb”. Originally, the length of an inch was defined as the length of the joint (last phalanx) of the thumb of a man's hand.

In metric, an inch is 2.54 cm.

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

Foot - in English means “foot”. During the period of historically first attempts to introduce legalized units, the foot was defined as “the average length of the steps of 16 people leaving from 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.

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

Typical for german land the system of ratios of the basic units of length is formulated in treatises on the marking of fields. According to these writings, four fingers are a palm, four palms are a foot, two feet are an elbow. Great distances in Germanic lands were measured in miles. The Great German Mile was approaching 7.3 kilometers in length, but it was only one of the many miles used in Germany. The German nautical mile used in the Baltic was approximately 10 km.

For a long time, people have been faced with the need to determine the distances, lengths of objects, time, areas, volumes, etc.

Measurements were needed in construction, trade, and astronomy, in fact, in any area of \u200b\u200blife. A very high measurement accuracy was needed during the construction of the Egyptian pyramids.

Figure: 0

The importance of measurements increased with the development of society and, in particular, with the development of science. And in order to measure, it was necessary to come up with units of various physical quantities. Let's remember, as it is written in the textbook: "To measure some quantity means to compare it with a homogeneous quantity, taken as a unit of this quantity."

The purpose of my work was to find out: what units of length and mass existed and exist now, what is their origin?

Vershok, elbow and other units ...

Measure everything that is measurable and make everything that is not measurable available. "
G. Galilei

The earliest units were subjective units. So, for example, sailors measured the path with pipes, that is, the distance that the ship travels during the time the sailor smokes his pipe. In Spain, a similar unit was a cigar, in Japan - a horse shoe, that is, the path that a horse traveled until a straw sole tied to its hooves worn out, replacing a horseshoe.

In the program of the Olympic Games of Ancient Hellas, there was a stage run. It has been established that the Greek stage (or stages) is the length of the stadium in Olympia - 192.27 m.Stages is equal to the distance that a person walks at a calm pace during the time from the appearance of the first ray of the sun, when it rises, until the moment when the disk of the sun is entirely above horizon. This time is approximately equal to two minutes ...

The Romans (185 cm), the Babylonians (about 195 cm), and the Egyptians (195 cm) had stages as a unit of measure for distance.

In Siberia, in ancient times, the measure of distances was used - beech. This is the distance at which a person ceases to see the bull's horns separately.

For many peoples, the unit of arrow length was used to determine the distance - the range of the arrow. Our expressions “keep out of a gun shot”, later “on a cannon shot” - remind of similar units of length.

The ancient Romans measured distances in steps or double steps (step with the left foot, step with the right). A thousand double steps was a mile (lat. Mille - a thousand).

The length of the rope or fabric is inconvenient to measure in steps or stages. The units found among many peoples, identified with the names of parts of the human body, turned out to be suitable for this. Elbow is the distance from the end of the fingers to the elbow joint.

Figure: Fig. 1 2

A measure of length for textiles, ropes, etc. winding materials, many peoples had a double cubit. We still use this measure to roughly estimate the length ...

In Russia, for a long time, an arshin was used as a unit of length (about 71 cm). This measure arose during trade with eastern countries (Persian, “arsh” - cubit). Numerous expressions: “As if an arshin swallowed”, “Measure by your own yardstick” and others - testify to its spread.

To measure shorter lengths, a span was used - the distance between the ends of the apart thumb and forefinger.

Figure: 3

A span or, as it was also called, a quarter (18 cm) was 1/4 of an arshin, and 1/16 of an arshin was equal to an vershok (4.4 cm).

A very common unit of length was a fathom. The first mention of it occurs in the XI century. Since 1554, the fathom is set equal to 3 arshins (2.13 m) and it receives the name of the royal (or eagle, printed), in contrast to the arbitrary ones - swing and scythe. The fly fathom - the span of the arms - is approximately 2.5 arshins. The fisherman, who shows what a big fish he missed, shows us the flywheel.

Figure: 4

Slanting fathom is the distance from the end of the right arm extended upwards to the toe of the left leg, it is approximately equal to 3.25 arshins.

Figure: five

Let's remember, as in fairy tales about giants: "Slanting fathom in the shoulders." The coincidence of the ancient Roman measure of length - the "architectural cane" and the Old Russian scythe fathoms is surprising: 248 cm. This refers to the fathom "from foot to hand oblique, from ground to ground." This fathom was determined by the length of the rope, one end of which was pressed by the foot to the ground, and the other was thrown over the arm of a standing person bent at the elbow and dropped again to the ground.

When the above-mentioned oblique sazhen is folded in four, we get the "Lithuanian cubit" (62 cm).

In the countries of Western Europe, it has long been used as units of inch (2.54 cm) - the length of the joint of the thumb (from the Dutch "inch" - thumb) and foot (30 cm) - the average length of a human foot (from the English "foot" - foot).

Figure: 6 Fig. 7

An elbow, an inch, a span, a fathom, an inch, a foot, etc. are very convenient for measurements, as they are always “at hand”. But the units of length corresponding to parts of the human body have a big drawback: different people have fingers, feet, etc., have different lengths. To get rid of the arbitrariness, in the XIV century. subjective units begin to be replaced by a set of objective units. So, for example, in 1324 in England a legal inch was established, equal to the length of three barley grains attached to each other, stretched out from the middle part of the ear. The foot was defined as the average foot length of sixteen people leaving the church, that is, by measuring random people, we tried to get a more constant value of one - the average foot length.

Figure: eight

What value do we determine by weighing a body on a beam balance?

It is not known which people and when invented the lever balance. It is possible that this was done by many peoples independently of each other, and their ease of use was the reason for their widespread adoption.

Figure: nine

When weighing on a beam balance, put the body to be weighed on one cup, and weights on the other. Weights are selected so as to establish balance. This balances the masses of the weighed body and weights. If the balanced weights are transferred, for example, to the Moon, where the body weight is 6 times less than on Earth, the balance will not be disturbed, since the weight of both bodies and weights on the Moon decreased by the same number of times, but the mass remained the same.

Therefore, weighing a body on a beam balance, we determine its mass, not its weight.

Units of mass, like units of length, were first established according to natural patterns. Most often by the mass of some seed. So, for example, the mass of precious stones was determined and is still determined in carats (0.2 g) - this is the mass of the seed of one of the types of beans.

Figure: ten

Later, the mass of water filling a vessel of a certain capacity was taken as a unit of mass. For example, in Ancient Babylon, talent was taken as a unit of mass - a mass of water filling such a vessel, from which water evenly flows through a hole of a certain size for one hour.

By the mass of grains or water, metal weights of different weights were made. They were used when weighing.

The weights, which served as a standard (sample), were kept in temples or government offices.

In Russia, the oldest unit of mass was the hryvnia (409.5 g). There is an assumption that this unit was brought to us from the East. Subsequently, she received the name of the pound. To determine large masses, a pood (16.38 kg) was used, and small - a spool (12.8 g).

In 1791 in France it was decided to create a decimal metric system of measures. The main quantities in this system were chosen length and mass.

The commission, which included the largest French scientists, proposed to take as a unit of length 1/40000000 part of the length of the earth's meridian passing through Paris . The astronomers Meshen and Delambert were entrusted with measuring the length of the meridian. The work lasted six years. Scientists measured the part of the meridian's length located between the cities of Dunkirk and Barcelona, \u200b\u200band then calculated the full length of a quarter of the meridian from the pole to the equator.

Figure: eleven

Based on their data, the standard of a new unit was made from platinum. . This unit was called meter - from the Greek word “metron”, which means “measure”.

Figure: 12

The mass of one cubic decimeter of distilled water at a temperature of its highest density of 4 ° C, determined by weighing in vacuum, was taken as a unit mass. The standard of this unit, called the kilogram, was made in the form of a platinum cylinder.

In 1869, the St. Petersburg Academy of Sciences appealed to scientific institutions all over the world with an appeal to make the decimal metric system of measures proposed by French scientists international. This appeal also said that "advances in science have led to the need to abandon the previous definition of the meter as 1/40000000 of a quarter of the length of the Parisian meridian, since the later more accurate measurements of the meridian gave different results." In addition, it became known that the length of the meridian changes over time. But since it was inconceivable to change the length of the meter after each measurement of the meridian, the St. Petersburg Academy of Sciences proposed to take the meter stored in the French archive (archival meter) as a prototype - the first sample and make from it as accurate and stable copies for different countries as possible, making this international metric system of measures.

When was the metric system of measures introduced in our country? Leading Russian scientists, who did a lot to make the metric system of measures international, could not overcome the resistance of the tsarist government to the introduction of the metric system of measures in our country. It was only possible to achieve that in 1899 a law was adopted, prepared by D.I.

The question of using the metric system of measures in Russia was finally resolved after the Great October Socialist Revolution. On September 14, 1918, the Council of People's Commissars of the RSFSR issued a decree, which said: "To base all measurements on the international metric system of measures and weights with decimal subdivisions and derivatives."