Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (1821-1894) was a prominent Russian mathematician, professor on algebra, number theory, và probability at St. Petersburg University and member of many Academies. His contributions khổng lồ the science include distribution of Prime number theory, prove of fundamental limit theorems in probability theory, theory of polynomial approximations lớn functions, theory of interpolation, the theory of moments & the approximate calculus of definite integrals và others.

Bạn đang xem: Chebyshev's theorem

Besides the mathematics, Chebyshev spent much of his time working on questions of mechanical engineering và in early 1870s he designed and manufactured very interesting calculating machines.

In 1876 Chebyshev made a report khổng lồ the French Association of Assistance to lớn Prosperity of Sciences about his first calculating machine. The report was called “An Adding Machine of Continuous Motion”. In the same 1876 the device was probably exhibited at the scientific meeting in Clermont-Ferrand.

It was a ten decimal places adding machine with a continuous tens carry, the first known machine with this type of carry mechanism. In a regular calculating with discrete carry, the wheel of higher rank moves on by one point, while the lower rank wheel moves from 9 to lớn 0. During the continuous tens carry, the wheel of higher rank moves from one point khổng lồ the next gradually and continuously, while the the lower rank wheel turns by one revolution. Hence, it is necessary to lớn have a construction such that the wheel of the tens moves 10 times slower than that of the units, the wheel of the hundreds moves 10 times slower than that of the tens, etc. This can be achieved with gears in a 1 lớn 10 ratio between the units và the tens, between the tens và the hundreds, and so on. This solution then totally dispenses with the usually complex mechanisms required for an intermittent motion. It also makes it possible to vì calculations much faster.Chebyshev reached this effect of gradual movement by implementing a planetary transmission (the same principle will be used 10 years later on by Eduard Selling).

Two years later Chebyshev created a second improved mã sản phẩm of his adding device, which was presented in 1878 to lớn *Conservatoire des Arts et Métiers* in Paris. Later, he made a dividing-multipying extension unit for the machine, which was also sent to the Paris museum in 1881. So the machine became a real arithmometre (it can be used for the all arithmetical operations), which has two separate blocks—one for addition and subtraction, and one for multiplication và division.

The main purpose of the machine was to demonstrate the new principle of continuous tens carry. The dividing-multipying unit also had some innovations, e.g. The automatic shifting of the carriage from decimal place khổng lồ decimal place. The unit itself served as the carriage part, that is the moving part of the mechanism. It was mounted on the adding machine, thus imposing one single device. To lớn perform multiplication, the operator only needed khổng lồ turn the handle. The number of turns was equal khổng lồ the sum of numbers of the multiplication factor, added khổng lồ the number of its decimal places minus one. After multiplying by a number (digit) of one decimal place, the mechanism automatically stopped multiplication và shifted the carriage lớn the next decimal place. This was repeated with the next decimal place digit, etc. The number of the handle turns was automatically controlled by means of a special counter, connected khổng lồ the mechanism for setting the factor.

The arithmometre of Chebyshev

Since the donation of the machine to lớn the museum was not followed by any publications in western media, this invention didn’t become famous (but the arithmometre was described in some Russian sources, for example this one from 1894). As late as 1890 the French mathematician François Édouard Anatole Lucas (one of the creators of the famous Genaille-Lucas rulers) displayed a variety of Chebyshev’s mechanisms, including the arithmometre, on a special stand at the Paris Museum & gave several lectures about Chebyshev. Later on the French historian Maurice d’Ocagne (1862-1938) contacted Chebyshev for description of the machine & published an article.

In fact, both machines of Chebyshev were made only for demonstration purposes. He never seriously thought of creating a device for practical or commercial use. His personal innovations are continuous tens carry và automatic shifting of the carriage from decimal place to lớn decimal place during multiplication (Chebyshev proved that this principles can help building extremely efficient machines). Both inventions became popular & were widely implemented in 1930s, when electromotive drives came into use in the quickly growing generation of automatic & semi-automatic keyboard calculating machines.

Xem thêm: Đề Thi Tiếng Anh Trình Độ A Có Đáp Án, Đề Trắc Nghiệm Tiếng Anh Trình Độ A Số 1

The arithmometre of Chebyshev

The adding machine of Chebyshev is an unusual calculating machine. Using gradual motion, it dispenses with carry levers & such, and allows for faster calculations. It is also a modular machine, in which an independent addition component becomes a sliding carriage of a larger multiplication machine. Chebyshev also automated the multiplication by one digit và the shift of the carriage, so that the user merely has khổng lồ rotate the crank and not worry about shifting when multiplying by numbers greater than 9.