"Odinitsі vimiru" - The impersonal loneliness osnuvalo and for vimiru masi. Hour. How many pennies does the penny have? Vimiryuvannya kutiv at degrees appeared over 3 yew. the fate of that at Babylon. Nil. Matrix entry system. Think, skilki pivshok in altini. So sazhen, likot, p'yad. Name the shots. Arithmometer and Great mathematicians.

“Single squares” - From the little one you can see that the rectangle is broken into single squares-klitini. What lesson is assigned? 1 a = 10m, b = 20m. 2 a = 5 cm. Mathematical hack. Point to the little one, like a figure is called a rectangle, and like a square? A square with a bagatokutnik

"The value of dozhini" - The problem is about the number of books. a. Butt: area, obsyag, masa, hour, vartіst ta kіlkіst commodities ta іn. a) Dovzhini vіdrіzka; b) Square figures; c) Masi tila? 2kg. A natural number is like the world's magnitude. E. A) 1200 m; b) 20 pieces c) 320 kg; d) 12 min.

"Math Lesson Decimeter" - 5 + 2 =. 12. 1) Take a small piece of wind. 13. 18. Decimeter. 19. 10. 7 tangerines were brought to obid mavpam, and kiwi - 3 less. 14. Mathematics lesson 1st grade Mikolaeva Nataliya Mikolayivna. We vmієmo rahuvati dozens. Reclaim the dozhina of the liani.

"Vidstan" - Vidstan - 510 km. The speed of the train is 90 km/year. Hour - ? Vidstan - 120 km. Bus speed - 60 km/year. Hour - ? At the rock of the Great Vitchiznyanoy Vіyny, the place saw a 900-day blockade. Founded by Peter Pershim. Rozrahunok hour change 1. Church of the Transfiguration of the Savior in the Illin. Buv roztashovaniya shlyakhіv "from the Varangians among the Greeks" on the stick.

"Decimeter of mathematics 1 class" - 2. Water is placed in the wind 10. Line. Katya has 2 less fish. Solve the task: The goals of the lesson. Writing the numbers of another ten. How many fish at Kolya? liters How many fish do Katya have? "Decimeter". 15 14 18 19 20 16 11 12. And in liters? kilograms. Dovzhina vіdrіzkіv. Physical culture. What kind of windfall? Centimeter.

Themes have 43 presentations in total

Before singing moment of its development, the people were satisfied with the natural “calculator” for the pіdrakhunka of objects — they gave ten fingers to the people. If they didn’t hang out, it happened to use different primitive instruments: curing stones, sticks, abacus, Chinese suan-pan, Japanese soroban, Russian rahunki. The power of these tools is primitive, the protection from them is not abusive. So, for example, for a modern person, who was born in the era of calculators, it is superficially easy to master the plurals and numbers on the robes. Such a diva of "kistyanoi" equilibrists at once under the force, perhaps, less than microprogrammers, assigned to the mystery of the robotic Intel microprocessor.

Having broken through the mechanization of the rahunka, if the European mathematicians began to find arithmometry ahead of the wine. However, almost a look at the varto from a fundamentally different class of enumerations.

dead end gilka

In 1614, the Scottish Baron John Napier (John Napier, 1550-1617) published a brilliant treatise "Description of the marvelous table of logarithms", which in the meantime had a revolutionary mathematical method. Grounded on the logarithmic law, mentally seeming, “replacing” the multiplier and arranging the additions and inferences, there were folded tables, which made it easier for the robot, first for everything, astronomers, who operate with great arrays of numbers.

A few hours later, Edmund Gunter (1581-1626) Valliets (Edmund Gunter, 1581-1626) for ease of calculation, having introduced a mechanical attachment, a kind of vicorist logarithmic scale. To the number of graduations according to the exponential law of the scales, two compasses were added to the scales, which it was necessary to operate at once, denoting the sum or the difference between the scales, which allowed to know the TV or private. Tsі manіpulyatsії vimagali pіdvishchenої respect.

In 1632, the English mathematicians William Oughtred (1575-1660) and Richard Delamain (1600-1644) blamed the logarithmic line, in the same scale one can see one another, and the circle has a circle. Moreover, the English propagated two designs: a rectangular one and a round one, in a logarithmic scale, were applied on two concentric rings, which wrap one or the other.

The "canonical" construction of the logarithmic line appeared in 1654 and was victorious in the world right up to the beginning of electronic calculators, the author of which was the English Robert Bissaker. Vіn uzyav three graduated planks with a length of 60 centimeters, creaking two zvіshnіshnі with a metal frame, and the middle bula vikoristana like a dvigun, which kovzav between them. The axis of only a runner, which fixed the result of a vikonan operation, did not transfer such a design. The great Sir Isaac Newton (1643-1727) spoke about the need for this, insanely, brown element in 1675, I’m still, English. However, it is absolutely fair that yoga was realized only after a hundred years.

It is necessary to note that the logarithmic method is calculated on the basis of the analog principle, if the numbers are "submitted" by their analogues, in this case - by doubles of the winds. Such an analogue is not discrete; This value is uninterrupted, which, unfortunately, may be a bad mistake, which is to blame for this death, that low accuracy of manifestation. For this purpose, for the help of a logarithmic line, it would be possible to work out, say, 10-bit numbers, and the debt is to reach ten dozen meters. I fully understood that the implementation of such a project is absolutely stupid.

On the same ideological principle, which is the logarithmic line, in the XX century, analog computing machines (AVM, analog computers) were created. The stench of the calculated value was represented by the electrical potential, and the calculation process of the model was provided with additional help. electric lansyug. Such outbuildings were made universal and allowed to carry out a lot of important tasks. The uninterrupted victory of AVM in pairs with digital machines of that hour was high on swedkodiya. The floorings are not transversely short - the accuracy of the results is low. If the 1980s had a hard time computer systems, The problem of shvidkodії became not such a state of affairs, and AVM gradually went into the darkness, although they did not appear on the face of the earth.

toothy arithmetic

At a superficial glance, one can surmise that the court of history is more mercilessly with a smaller type of calculating mechanisms - with arithmometers. True, at the same time you can learn more from the museum. For example, at our Polytechnic, or at the German Museum in Munich (Deutches Museum), or at the Museum of Computing Technology in Hannover (Ponton Computer-Museum). However, it is fundamentally wrong. Based on the principles of diary arithmometers (bit by bit addition and sum of private creations), there were created electronic arithmetic additions, the “head” of the EOM. Over the years, the stench has overgrown with an annex of control, a memory, a periphery, and, to be sure, they have been walled into the processor.

One of the first arithmometers, to be more precise, “the imaginary machine”, was found by Leonardo da Vinci (1452-1519) close to 1500. Truth is, about yoga ideas, no one knows how much to stretch out. I’ll build a little baby of some kind only in 1967, and in a new way, IBM has created a completely practical 13-bit machine, which is based on the principle of 10-tooth wheels.

Ten years earlier, as a result of historical investigations in Nimechchina, a chair was revealed that description of an adding machine, vikonan in 1623 by Wilhelm Schickard (1592-1636), professor of mathematics at the University of Tübingen. The whole bula was “put in” a 6-bit machine, which was formed from three nodes: an attachment for folding-out, a multiplication attachment and a block for recording intermediate results. Just like the accumulator of the letters of vikonations on traditional gear wheels, which small cams for transmission to the judicial order of one transferred, then the multiplier of letters of inducements has already been thinned out. In a new German professor, having planted the “Grat” method, if, behind the help of “planted” on the shaft of the toothed “multiplication table”, the skin number of the first multiplier is multiplied by the skin number of another, after which all the private creations are summed up.

This model seemed to be practical, which was brought up in 1957, if it was done in the FRN. It is unbelievable that Shikkard himself could induce his adding machine. Є svіdchennya, yak vengeance at yoga listing with the astronomer Johannes Kepler (Johannes Kepler, 1571-1630) due to the fact that the unfinished model died at the fire for an hour later in the main. Before that, the author, who had died of cholera, did not get into scientific knowledge about his wines, and it became less known about him in the middle of the 20th century.

Tom Blaise Pascal (Blaise Pascal, 1623-1662), who was not the first to construct, but also inspired a practical adding machine, starting, as it seems, from scratch. Brilliant French scholar, one of the creators of the theory of immorality, the author of many important mathematical theorems, a legacy of nature, who discovered the atmospheric pressure and determined the mass of the earth's atmosphere, and a prominent thinker, who, having lost such a mind, did not spend it on himself until today to the provincial”, as a beloved son of the President of the Royal House of Assembly to everyday life. Nineteenteenth century youth, in 1642, roci, helping the fathers, who spent a lot of time and strength, adding up finances, constructing a car, yak could add up the same numbers.

The first star was gradually broken, and in two years Pascal had completed a perfect model. This was the day of the financial machine: it was small six tenth rows and two additional ones: one subdivision into 20 parts, the other by 12, which led to the spiving of those penny units (1 sou = 1/20 livre, 1 day = 1/12 sou). The skin category was given a wheel with a singing number of teeth.

For his short life, Blaise Pascal, having lived a total of 39 years, made close to fifty rahunkov machines from the most versatile materials: from midi, from different types of wood, from elephant brushes. One of them was a lecture given to Chancellor Seg'e (Pier Seguier, 1588-1672), as a model of sales, as if demonstrating for an hour of lectures on the remaining achievements of mathematical science. 8 copies have reached our days.

Pascal himself should have the first patent for "Pascal's wheel", visions of the year 1649 by the French king. As a sign of honor to the yogi of merit in the gallery of "calculative science", one of the current programming methods was named Pascal.

Modernizers

It was fully understood that "Pascal's Wheel" spurred the wine-makers to the perfection of the subsuming machine. Claude Perrault (Claude Perrault, 1613-1688), the brother of the all-worldly known Cossack, who was a man of the widest interests and unique interests, sings even an original solution. At the creative car of Claude Perrault, there are dated 1670 rock armchairs for summing up the machine; With progressive Russian, the stench wraps the lichil sumi.

Come constructor's word - and yake! - Having said Gottfried Leibniz (Gottfried Leibniz, 1646-1716), redevelopment of merit and take what can be replaced by two words "great thinker". Vіn having grown rich in mathematicians, that the “father of cybernetics” Norbert Wiener (Norbert Wiener, 1894-1964) proponed the canonization of the German scientist and “appointed” to the saints what to give to the creators of computers.

The first arithmometer Leibnitz prepared in 1673 roci. After that, 20 years later, having taken up the perfection of his medical machine. The 8-bit model could add, see, multiply, divide, and step on the results of a stressed search. The result of the multiplication is the submultiple of 16 characters. Leibniz zastosuvav in his arithmometer constructive elements, as victorious in the design of new models right up to the twentieth century. Before them, first of all, it is necessary to carry a loose carriage, which made it possible to increase the speed of the multiplication. The control of the car was marginally simple for the hand of the arm, for the help of which the rolls were wrapped, that automatic control of the number of private creations was added to the hour of production.

In the 17th century, obviously, one could not talk about the serial production of Leibnitz's arithmometers. However, not so little was released. So, for example, one of the models was given to Peter I. The Russian tsar, having ordered the mathematical machine to do it in his own way: having presented it to the Chinese emperor for diplomatic purposes.

A glance at constructive ideas related to the improvement of mechanical medical machines is incomprehensible without riddles about the Italian mathematics of Giovanni Poleni (1683-1761). I founded my scientific activity as a professor of astronomy at the University of Padua. Then we moved to the Department of Physics. І unexpectedly having taken the chair of mathematics, having replaced Mykola Bernoulli (Nicholaus Bernoulli, 1695-1726) in the tsіy settlement. His hobbies are architecture, archeology and the construction of clever mechanisms. In 1709 Poleny demonstrated an arithmometer, in a way that was based on the progressive principle of "a gear wheel with a variable number of teeth." A new and important innovation was brought to the new one: the machine was brought into action by the force of a falling vantage, tied to a free rope. The first story of "arithmometer-budding" was the first attempt to replace the manual drive with a splendid energy source.

And in the 1820s, the English mathematician Charles Babbage (Charles Babbage, 1791-1871) wrote “I Carry a Car” and started life. For the life of Babbage, this apparatus was never prompted, but, more importantly, if the financing of the project ended, the mathematician predicted the "Analytical Engine" for high-level calculations, and first formalized it by describing the logic ... of the computer. Ale, vtim, tse already troch іnsha іstorіya.

Great series

In the 19th century, if the technology of precise processing of metals reached significant successes, it became possible to use an arithmometer in the most highly manipulative sphere of human activity, in which, as it is now customary to say, it is necessary to process a great array of data. Charles-Xavier Thomas de Colmar (1785-1870) became the pioneer of serial production of rahunkov machines. Introduced into the Leibniz model a number of operational improvements, in 1821 the company began to release 16-digit arithmometers from its Parisian master, yakі gaining popularity like "thomas-machine". A bunch of stench was costly - 400 francs. I were issued in not so great numbers - up to 100 copies per river. And before the end of the century, new pickers appear, because of competition, prices are reduced, and the number of buyers is growing.

Different designers, like the Old and the New Lights, patent their models, as they look like the classic Leibnitz model, without introducing additional efficiencies in operation. There is a call, which signals about pardons to the type of a smaller number of a larger one. Dial important are replaced by buttons. To fight the pen for transferring the adding machine from place to place. Ergonomic displays are moving forward. Vdoskonalyuetsya design.

For example, in the 19th century, Russia invaded the world market of arithmometers in the highest order. The Russian-born Swede Wilgodt Teofilovich Odner (1846-1905), a talented winemaker and a happy businessman, became the author of this breakthrough. Prior to starting the issuance of private cars, Vilgodt Teofilovich designed an attachment for automated numbering of banknotes, which stopped the process of printing papers. You should be credited with the authorship of a machine for stuffing cigarettes, an automatic ballot box for the State Duma, as well as turnstiles, which were used by all shipping companies in Russia.

In 1875, Odner designed his first adding machine, transferring the rights to manufacture it to the Ludwig Nobel machine plant. After 15 years, having become the head of the master, Vilgodt Teofilovich launches a new model of an adding machine in St. Petersburg, as it is visible in the form of medical machines, which were known at that time, compactness, reliability, simplicity in a corystuvannya and viscous.

After three years, the minesternya becomes a hard factory, which vibrates over 5 thousand arithmometers for a river. With the stamp "Mechanical Plant V.T. At the beginning of the 20th century, Odner's adding machine began to dominate the world market.

After the rapt death of "Russian Bill Gates" in 1905, Odner's relatives were continued by his relatives and friends. Revolution put an end to the Slavic history of the company: V.T. Odner Bulo converted to a repair plant.

However, in the mid-1920s, the release of arithmometers in Russia was revived. The most popular model, which took the name Felix, was produced at the factory. Dzerzhinsky is left in the 1960s. Simultaneously with Felix, the production of electromechanical medical machines of the VK series was improved at the Radyansk Union, and for some types of medical machines, they were replaced by an electric drive. Tsey type counting was created for the image of that likeness of the German car "Mercedes". Electromechanical machines are paired with arithmometers for little significantly greater productivity. However, the gurkit, which was created by them, looked like a shooter from a machine gun. While in the operating room there were about two dozen Mercedes, then in the noise environment it was a scorched beating.

In the 1970s, when electronic calculators began to appear - a handful of lamps, then transistor ones - all the more mechanical writing began to move rapidly to museums, and then to change.

The first side of the history of the creation of counting machines is related to the names of the French philosopher, writer, mathematician and physicist Blaise Pascal. In 1641-42, roci vin constructed a mechanical calculation, which allowed adding up and counting numbers.

In 1673, Gottfried Leibnitz, a German scholar, prompted the first lachrymator and created all the arithmetics. Vaughn became the prototype of arithmometers. During the 19th century, a rich construction of arithmometers was created, their reliability and accuracy of calculation were promoted. The stench of the nabuli is wider than wide.

This deposit was made by high-ranking designers of Russia: Yakobson, Slobidsky, Stoffel, Kummer, Chebishev. In 1878, the rotation of the Russian teachings P. Chebishev propagated a lіchlnu machine, which was completed by adding that vіdnіmannya of richly significant numbers.

Petersburg engineer Odner Vinayshov arithmometer with gear, which can change the number of teeth. The yogo design appeared on the flooring thoroughly, (the attachment allowed you to finish all the chotiri arithmetic diї) which arithmometric type was issued in 1873 for a hundred years. In the 30s of the 20th century, our country developed a perfect arithmometer – “Felix”. Tsіlіlnі pіstrії vikoristovuvalysya kіlі ten years.

At the beginning of the 19th century (1823 - 1834), the English mathematician Charles Bebbij formulated the main theses, which may form the basis for the construction of a calculating machine of a fundamentally new type. Ideas for the design of the machine including the main extensions of counting machines: memory, arithmetic extension, keruvane extension, input-output extension. Implementation of the project for the purpose of the machine did not go far through the low development of the machine industry. However, the number of programs for this machine was created by George Byron's daughter Ada Lovelace, as the first programmer is respected.

Less than 100 years later, in the 40s of the 20th century, it was possible to create a programmed medical machine based on an electromechanical relay. Qi cars did not manage to get started in serial production, as the first EOMs based on radio lamps appeared.

The first EOM "Yeniak" was created in the USA in 1946. The group of creators included the famous teachings of the 20th century, John von Neumann, who propagated the main ambush of the EOM: transition to the dual number system for the presentation of information and the principle of saving programs. The program was calculated by placing it in the EOM memory, which would ensure the automatic mode of typing commands and, as a result, the improvement of the EOM code.

Over the course of an hour, they worked on EOM projects in England and Russia, de first EOM, which took the name MESM (small electronic rahunkov machine) was broken up in 1950, and first great EOM - BESM in 1952. From which moment a burkhlivy development appeared counting technique. You can see five steps in the development of electronic counting machines.

o 40-50 years of the 20th century - the first EOM in the USA and the SRSR;

o 50-60 years of the 20th century - the first movie programming;

o 60-70 years of the 20th century - first ACS, CAD, EU EOM;

o 70-80 years of the 20th century - Persian personal computers;

o 80-90 years of the 20th century - mass stagnation of personal computers.

In the history of computational technology, one can mentally see three stages:

1. home-mechanical;
2. mechanical;

Three periods include the entire evolution of the calculation of people, starting from the rahunka on the fingers to the calculation on the current over-stretched computers.

Pre-mechanical period

Let's look at the pre-mechanical period: the whole period, the shards of the wines of the month right up to the 17th (!) century.

Among wealthy peoples, the number of fingers (5, 10, 15 and 20), which were used for counting, became a base for five, ten, five and twenty systems of numbers.

Abacus

Stones (or sticks) came to change the fingers, as they were placed in a container for the clarity of the rahunka.

In the 5th century BC in Greece and Egypt, the wide abacus was widened, which is shifted from the walnut like a medicine board. Calculations for abacus were carried out by moving chimneys with chutes on special boards.

Similar counting tools expanded and developed throughout the world. For example, the Chinese version of the abacus was called suan-pan.

Russian rahunki

With the help of an abacus you can also use Russian rahunki. In Russia її z'appeared between the 16th-17th centuries. And the stench was victorious until the 21st century.

Russian rahunki

Rocky 15 that foreigners hooted, if rakhunks were pumping in us someday. Aje stink of such an attachment for counting bouv. At cob classes at schools, rahuvati was taught on rahuvati here until 1970.

Mechanical era

Now, in the pre-mechanical period of the history of calculating technology, let's move on to the mechanical one.

Pascal's subsuming machine

In 1642 p. Frenchman Blaise Pascal, a great mathematician and physicist, created the first medical machine in 19 years. There is a mechanical attachment at the sight of the screen, which is composed of numerical gears, tied one by one.

He was doing a lot of work in order to make it easier for the robot of Yogo Batka - the picker of gifts, who had to spend a long time with timid roses from gifts.

Pascal machine

Pascal's machine followed this principle: when the wheel of a smaller order is turned again, the mechanism turns the wheel of a larger order by one. So it is on the rahunkah: if the youngest rank of the brushes is completed, then the brush is added to the senior rank.

The principle of linking columns, layings by Pascal, mayzhe for the 3rd century, becoming the basis for the creation of offensive modifications of counting outbuildings.

Leibniz arithmometer

In 1673 p. the great mathematician Gottfried Leibniz, having developed the idea of ​​Pascal, having created a mechanical adding machine, on which it was possible to perform all arithmetic operations with richly significant numbers:

1. dodavannya,
2. vіdnіmannya,
3. plural that
4. rozpodіl.

Arithmometer Feliks

At 1880 p. Russian winemaker V.T.

Ponad those, 1890 having made a mass release of arithmometers, they knew that they were stuck in the world.

Arithmometer Feliks

The SRSR has the widest arithmometer "Felix", which ranks among the most important arithmometers of Odner. Vіn vypuskavsya at the factories of medical machines near Penza, Kursk and Moscow from 1929 to 1978 r.b.

Instructions for folding and multiplying on Felix arithmometer

shob fold two numbers on the Felix arithmometer, follow the same way:

1. Install the first dodanok on the calipers of the adding machine.
2. Turn the handle in front of yourself (for the year's arrow). When this number is important, it is important to enter into the account of the sum.
3. Vistavte another dodanok on the wads.
4. Turn the handle towards yourself. With which number on the vazhel will reach the lichnik pіdsumovuvannya.
5. The result of the folding is for the lichnik pіdsumovuvannya.

shob multiply on a small number on the Felix arithmometer, work out the following:

1. Put the first multiplier on the important arithmometer.
2. Turn the handle in front of yourself until another multiplier appears on the spinner.
3. The result of the multiplication is for the lichilnik pіdsumovuvannya.

Like bachite, everything is simple with an adding machine: You turn the knob, and the machine is smart for you!

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for those who drink

Adding machine

Passing an hour, and consume people in the processing of numerical information grown. The first ideas of mechanization of the counting process were called, for example, the XV - the beginning of the XVI century. About the evidence of knowledge, for example, the 60s of the last century, the sketches of summation, the development of Leonardo da Vinci.

In the 17th century of physics, that astronomers stumbled over the necessary creation of folding and bulky calculations. We will need cars, buildings, and count a great deal in a short hour and with high accuracy.

In 1642, the young Frenchman Blaise Pascal, who became a famous physicist and mathematician in the near future, created and won the great popularity of the first mechanical calculating machine - an adding machine. Rakhunkov's car of Pascal bula is similar to a small screen, on the krishtsi, as if on a birthday, there were ruffled dials. There i set the numbers. For the numbers of different rows, different wheel gears were introduced. The skin of the front wheel kicked up behind the stepping one for the help of one tooth. The whole cog entered at the hooked with the chergovy wheel only after all nine digits of this order had passed. Come on, for example, up to six, five fives are added, then the wheel alone can be crushed at the sum of 11 krokiv; at the position "0", the next step after the position "9" should be attached to the wheel of ten and turn it by one tooth. As a result, the wheels will show the number 11.

In the three centuries that have passed since the creation of the first arithmometer, there have been created close to a hundred different types of mechanical machines and machines. Most of these wines have already been forgotten. Ale buli and so wine walkers, as they became important pods in the history of counting machines.

In 1677, the great German mathematician and philosopher Gottfried Wilhelm Leibnitz constructed his lathe machine, which allowed not only to add up and see, but also to multiply and dility richly significant numbers. At his arithmometer Leibnitz victoriously replaced the wheels of the cylinder. Numbers were applied to the cylinders. Leather cylinder mav nine rows of ridges: one ridge - at the first row, two - at the other, and so on until the ninth, to avenge nine ridges. The cylinders were friable and were restored to the same position by the operator.

The great deposit at the perfection of the rakhunk machines was made by the Russian high schools and engineers. So the adding machine, created in 1874 by the Russian engineer Odner, successfully competed with the largest adding machines of European companies and known zastosuvannya in the world. Yogo modification "Felix" was produced in our country until the 50s of the XX century.

Arithmometry long hour Mali is a serious shortfall: I calculated the result manually by writing it down on an arkush paper. The time has come to talk about those, that the lichlna machine itself was writing on the paper, it’s more that the drukar’s machine was already found guilty. І axis at 1889, the first medical machine appeared, secured by a different outbuilding.