Who defined the word addition? The history of the emergence of arithmetic operations. Examples of the use of the word addition in literature

Description of the presentation by individual slides:

1 slide

Slide description:

History of the origin of mathematical signs Prepared by: Ivan Cherepanov, student 5th grade Mathematics teacher: O.A. Mosunova Just as there is no table without legs in the world, Just as there are no goats in the world without horns, Cats without mustaches and without the shells of crayfish, So there are no operations in arithmetic without signs!

2 slide

Slide description:

3 slide

Slide description:

Objectives Consider where mathematical signs came to us and what they originally meant. Compare mathematical signs of different nations. Consider the similarity of modern mathematical signs with the signs of our ancestors

4 slide

Slide description:

Object: mathematical signs of different peoples Main research methods: literature analysis, comparison, survey of students, analysis and synthesis of data obtained during the study.

5 slide

Slide description:

Why in our time do we use exactly these mathematical signs: + “plus”, - “minus”, ∙ “multiplication” and “division”, and not some others? Problem

6 slide

Slide description:

Hypothesis I think that mathematical signs arose simultaneously with the advent of numbers and numbers

7 slide

Slide description:

Origin of mathematical symbols The origin of these symbols cannot always be accurately determined. The symbols for the arithmetic operations of addition (plus “+’’) and subtraction (minus “-‘’) are so common that we almost never think about the fact that they did not always exist. Indeed, someone must have invented these symbols (or at least others that later evolved into the ones we use today). It probably also took some time before these symbols became generally accepted. There is an opinion that the signs “+” and “–” arose in trading practice. The wine merchant marked with dashes how many measures of wine he sold from the barrel. By adding new supplies to the barrel, he crossed out as many expendable lines as he restored. This is how the signs of addition and subtraction allegedly originated in the 15th century. There is another explanation regarding the origin of the “+” sign. Instead of “a + b” they wrote “a and b”, in Latin “a et b”. Since the word “et” (“and”) had to be written very often, they began to shorten it: first they wrote one letter t, which eventually turned into a “+” sign

8 slide

Slide description:

Algebraic sign “-” The first use of the modern algebraic sign “+” refers to a German algebra manuscript of 1481, which was found in the Dresden library. In a Latin manuscript from the same time (also from the Dresden library), there are both symbols: + and -. It is known that Johann Widmann reviewed and commented on both of these manuscripts. In 1489, he published the first printed book in Leipzig (Mercantile Arithmetic - “Commercial Arithmetic”), in which both signs + and - were present (see figure). The fact that Widmann used these symbols as if they were common knowledge points to the possibility of their origins in trade. An anonymous manuscript, apparently written around the same time, also contains the same symbols, and this led to two additional books published in 1518 and 1525.

Slide 9

Slide description:

Some mathematicians, such as Record, Harriot and Descartes, used the same sign. Others (such as Hume, Huygens, and Fermat) used the Latin cross “†’’, sometimes placed horizontally, with a crossbar at one end or the other. Finally, some (such as Halley) used more decorative look Widman

10 slide

Slide description:

First appearance of "+" and "-" on English language discovered in the 1551 algebra book “The Whetstone of Witte” by Oxford mathematician Robert Record, who also introduced the equals sign, which was much longer than the current sign. In describing the plus and minus signs, Record wrote: “Other two signs are often used, the first of which is written “+” and means more, and the second “-” and means less.”

11 slide

Slide description:

Subtraction sign Subtraction symbols were somewhat less fancy, but perhaps more confusing (to us at least), since instead of the simple “-” sign, German, Swiss and Dutch books sometimes used the symbol “÷'', which we now use denote division. Several seventeenth-century books (such as Halley and Mersenne) use two dots “∙ ∙’’ or three dots “∙ ∙ ∙’’ to indicate subtraction.

12 slide

Slide description:

In Ancient Egypt In the famous Egyptian papyrus of Ahmes, a pair of legs going forward signifies addition, and those going away signify subtraction

Slide 13

Slide description:

The ancient Greeks indicated addition by side notation, but occasionally used the slash symbol “/'' and a semi-elliptic curve for subtraction. The Hindus, like the Greeks, generally did not represent addition in any way other than using the symbols "yu'' used in Bakhshali's manuscript “Arithmetic” (probably third or fourth century).

Slide 14

Slide description:

In the late fifteenth century, the French mathematician Chuquet (1484) and the Italian Pacioli (1494) used “p” (denoting “plus”) for addition and “m” (denoting “minus”) for subtraction. Shuke

15 slide

Slide description:

In Italy In Italy, the symbols "+" and "-" were adopted by the astronomer Christopher Clavius ​​(a German who lived in Rome), the mathematicians Gloriosi and Cavalieri in the early seventeenth century Christopher Clavius

16 slide

Slide description:

Multiplication sign To denote the action of multiplication, some of the European mathematicians of the 16th century used the letter M, which was the initial letter in the Latin word for increase, multiplication - animation (from this word the name “cartoon” comes). In the 17th century, some mathematicians began to denote multiplication with an oblique cross “×”, while others used a dot for this. In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in works of the 11th century. For thousands of years, the action of division was not indicated by signs. The Arabs introduced the line “/” to indicate division. It was adopted from the Arabs in the 13th century by the Italian mathematician Fibonacci. He was the first to use the term “private”. The colon sign ":" to indicate division came into use at the end of the 17th century. In Russia, the names “divisible”, “divisor”, “quotient” were first introduced by L.F. Magnitsky at the beginning of the 18th century. The multiplication sign was introduced in 1631 by William Oughtred (England) in the form of an oblique cross. Before him, the letter M was used. Later, Leibniz replaced the cross with a dot (late 17th century) so as not to confuse it with the letter x; before him, such symbolism was found in Regiomontan (XV century) and the English scientist Thomas Harriot (1560-1621).

Slide 17

Slide description:

Oughtred preferred the slash "/" for division signs. Leibniz began to denote division with a colon. Before them, the letter D was also often used. Starting with Fibonacci, the fraction line, which was used in Arabic writings, is also used. In England and the USA, the symbol ÷ (obelus), which was proposed by Johann Rahn and John Pell in the middle of the 17th century, became widespread.

18 slide

Slide description:

Equal and inequality signs The equal sign was indicated in different times in different ways: both in words and in various symbols. The “=” sign, so convenient and understandable now, came into general use only in the 18th century. And this sign was proposed by the English author of an algebra textbook, Robert Ricord, to indicate the equality of two expressions in 1557. He explained that there is nothing more equal in the world than two parallel segments of the same length. In continental Europe, the equal sign was introduced by Leibniz. The “not equal” sign was first used by Euler. Comparative signs were introduced by Thomas Harriot in his work, published posthumously in 1631. Before him they wrote with the words: more, less.

Explanatory Dictionary of the Living Great Russian Language by Vladimir Dahl

Addition, add up, complex, etc. see add up.

Ozhegov's Explanatory Dictionary

Addition, -i, cf.

see fold.

A mathematical operation by which from two or more numbers (or quantities) a new one is obtained containing as many units (or quantities) as were in all given numbers (quantities) together. Problem on p.

A word formed according to the method of composition (special). , -I, Wed. Same as body type. Bogatyrskoe village

Explanatory Dictionary of the Russian Language by Ushakov

ADDITION, addition, cf.

Units only action according to verb. add 2, 5 and 7 digits. - fold - fold. Addition of forces (replacement of several forces with one that produces an equivalent effect; physical). Addition of quantities. Resignation of responsibilities.

Units only One of four arithmetic operations, by means of which two or more numbers (addends) are used to obtain a new one (sum), containing as many units as were in all given numbers together. Addition rule. Addition problem. Perform addition.

Same as physique; general physical condition of the body. He was a hefty little guy with a heroic build. Nekrasov. I don’t boast about my build, but I am vigorous and fresh, and lived to see my gray hairs. Griboyedov. || Structure of matter (special). Spongy build.

There is an action by which the set of given numbers is reduced to the form a010n + a110n-1+ a210n-2 +.. . + an+an+110-1 + an+210-2 +.. . where all coefficients are less than ten. Everyone knows how to perform this transformation, and therefore we do not consider it necessary to go into details. D.S. Encyclopedic Dictionary of Brockhaus and Efron

Alexander Tsygankov, 4th grade student, Secondary School No. 7, Mirny

In mathematics lessons, we constantly work with one of the mathematical actions - addition, and we wondered when people first began to add, who and when gave names to the components of this action, and what else interesting you can learn about the action of addition.

Download:

Preview:

Message for Math Lesson

HISTORY OF THE ACTION OF ADDITION FROM ANCIENT TIMES TO THE PRESENT DAYS.

In mathematics lessons, we constantly work with one of the mathematical actions - addition, and we wondered when people first began to add, who and when gave names to the components of this action, and what else interesting you can learn about the action of addition.

Gradually we learned that everyone needs mathematics Everyday life. Everyone has to count in life; we often use (without noticing it) knowledge about the quantities of length, time, and mass. We realized that mathematics is an important part of human culture.

This paper examines a number of interesting questions about the action of addition as one of the basic arithmetic operations.

Since ancient times, people have been counting objects. People have been learning to perform arithmetic operations for more than a thousand years.

Human fingers were not only the first calculating device, but also the first computing machine. Nature itself provided man with this universal counting tool. For many peoples, fingers (or their joints) played the role of the first counting device in any trade transactions. For most of the people's everyday needs, their help was quite enough.

However, the calculation results were recorded different ways : notching, counting sticks, knots, etc. For example, knot counting was highly developed among the peoples of pre-Columbian America. Moreover, the system of nodules also served as storage and chronicle, having a rather complex structure. However, using it required good memory training.

Many number systems go back to finger counting, for example, pentary (one hand), decimal (two hands), decimal (fingers and toes), magnum (total number of fingers and toes for the buyer and seller). For many peoples, fingers remained a counting instrument for a long time, even at the highest levels of development.

Famous medieval mathematicians recommended finger counting as an auxiliary tool, which allows quite efficient systems accounts.

However, in different countries and at different times they considered it differently.

Despite the fact that among many peoples the hand is a synonym and the actual basis of the numeral “five,” among different peoples, when counting with fingers from one to five, the index and thumb can have different meanings.

Italians count on their fingers thumb indicates the number 1, and the index finger indicates the number 2; when the Americans and the British count, the index finger means the number 1, and the middle finger - 2, in this case the thumb represents the number 5. And the Russians start counting on their fingers, bending the little finger first, and end with the thumb, indicating the number 5, while the index the finger was compared with the number 4. But when the number is shown, the index finger is put out, then the middle and ring finger.

Each nation had its own arithmetic operations. And they were all used to perform operations on numbers. For a long time, people performed addition of numbers only orally with the help of some objects - fingers, pebbles, shells, beans, sticks.

In ancient India they found a way to add numbers in writing. When calculating, they wrote down numbers with a stick on sand poured onto a special board.

Indian sages suggested writing numbers in a column - one below the other; The answer is written down below.

In ancient China, addition was done on a board using special sticks. They were made from bamboo or ivory.

IN Ancient Egypt for addition, a hieroglyph in the form of walking legs was used. The direction of the legs coincided with the direction of the letter, which means that you need to perform addition.

IN Ancient Rus' Russian people in their calculations used only two arithmetic operations - addition and subtraction and called them doubling and bifurcation.

Some signs for addition appeared in antiquity, but until the 15th century there was almost no generally accepted sign. There are several points of view on how the sign for addition appeared.

In the 15th – 16th centuries, the Latin letter “P” was used for the addition sign, initial letter words plus. Gradually, this letter began to be written with two dashes. The Latin word " et" (et) , standing for "I", which means "more". Since the word “et” had to be written very often, they began to shorten it: first they wrote one letter “t”, which gradually turned into the sign “+ ». There is a third opinion: the “+” sign originated in trading practice.

The “+” sign first appears in print in the book “A Quick and Beautiful Account for Merchants.” It was written by the Czech mathematician Jan Widmann in 1489.

Man has always sought to simplify and speed up the solution of expressions, and this led to the creation of computing devices. Ancient peoples used the abacus calculating device for calculations.

Abacus is a counting board used for arithmetic calculations in Ancient Greece and Rome. The abacus board was divided into strips by lines; counting was carried out using 5 stones and bones placed on the strips. In China and Japan, oriental abaci made of 7 stones were common: Chinese suan-pan and Japanese - soroban.

Russian abacus - abacus, appeared at the end of the 15th century. They have horizontal knitting needles with bones and are based on the decimal system. Russian abacus was widely used for calculations. They are easy and quick to add and subtract.

For almost three centuries, talented scientists, engineers and designers have created mechanical calculating machines that make it easier to perform four mathematical operations.

At the beginning of the 19th century, the French inventor Carl Thomas took advantage of the ideas of the famous German scientist Leibniz and invented a calculating machine for performing 4 arithmetic operations and called it an arithmometer. Adding machines until the early 1970s. remained good assistants to computer scientists of all countries.

And 20 years ago, small devices were made that performed complex calculations in a matter of seconds - calculators. A calculator is an electronic computing device. Calculators can be desktop or (pocket) calculators built into computers, cell phones, and even wristwatches. But a computer performs various mathematical operations even faster than a calculator. All these are human assistants when counting. Despite all the advantages of the computer age, there is the fact that many adults have forgotten how to count without a calculator. And many children even count on their fingers - this is very inconvenient. Therefore, I propose to learn to count “like an adult”, using mathematical techniques - ways to memorize the table of addition within 20 and quickly count without a calculator and fingers. Clever math tricks will allow you to add in your head instantly. At first glance, these techniques seem confusing and incomprehensible. But once you understand them and bring their implementation to automaticity, you will understand how simple, convenient and easy these techniques are. Count faster, count better!

From interviews with subject teachers, we learned that the action of addition is actively used in other sciences.

Russian language . Topic: “Word Formation” (primary school teacher)

As a result of addition, a complex word is formed with several roots: snowfall, cinema, forest park.

Biology . Topic: “Human nutrition” (biology teacher)

Calorie addition is performed to determine the energy value of the product (proteins, fats, carbohydrates)

Geography . Topic: “Climate” (geography teacher)

Temperatures for a certain period are added up to find the average daily, average monthly, average annual temperature.

Physics . Topic “Interference” (physics teacher)

The addition of two (or several) waves in space, which results in an increase or decrease in the amplitude of the wave at different points - wave interference.

We can see the action of addition everywhere: in the construction of houses, in the design and construction of rockets, cars, in sewing clothes, in preparing dishes, in raising animals, in making medicines, and in many other areas of activity.

Conclusions :

• the action of addition has been used for a long time to count various objects
• the action of addition is used in many sciences
• most often in life both adults and children use addition
• The easiest way to add numbers is on a calculator
• there are “easy” ways to mentally count when adding