History of logarithms of presentation. The history of logarithms and their stagnation. Presentation on the topic: History of logarithms

An important study of logarithms was made by the Belgian mathematician Gregory of Saint-Vincent (1647), who discovered the connections between logarithms and areas, surrounded by an arc of hyperbola, all the abscissa and various ordinates. The presentation of the logarithm with an unskewed state series was given by M. Mercator (1668), who knew that In(1+x) = x Nezabar then J. Gregory (1668) opened the curved layout ln This series converges very quickly, since M = N + 1 and N sufficiently great; You can also use this method to calculate logarithms. The work of L. Euler was of great importance in the development of the theory of the logarithm. They introduced the concept of logarithm as a factor, turning it into a step.

LEONARD EULER ()

Well, already in the middle of the 16th century. the basics of learning about logarithms were discussed. However, there was a lack of clear, concrete methods for the broad practical application of these fundamentals in calculative mathematics, and there was no basis for understanding the idea of ​​logarithmic tables. For example, XVI century. Simon Stevin published a table for calculating folding sums, the need for calculating them was due to the growth of trade and financial transactions. Apparently, the formula for folding frames is as follows: A = a (1 + (p / 100)) t where a is the initial capital, A is the growing capital after t rocks at P%. Stevin’s table showed the values ​​of expressions (1+(p/100))t, and (p/100) =r Stevin also expressed in tens fractions: 0.04; 0.05;..., as the wines are more open in Europe. Stevin himself, astonishingly, did not note that tables can be used to simplify the calculations. Having learned this, however, one of his companions - Byurgi

Vinakhid of logarithms on the cob of the 17th century. tightly knitted with a scroll in the 16th century. science and trade, astronomy and navigation, which required the improvement of the methods of calculative mathematics. More and more often it is necessary to perform cumbersome operations on large-valued numbers, and the results of these actions become more and more precise. This is where the idea of ​​logarithms was introduced, the value of which lies in the reduction of the complex actions of the third stage (reduced to a step and the development of the root) to the more simple ones of the second stage (multiplying and subdividing), and the remaining ones - to simplest, up to stage I ( Folding and lifting).

The first tables of logarithms were created by the Scottish mathematician J. Napier and the Swiss I. Burgs (1552 - 1632 (about 8 rocks spent on this work). Englishman Henry Briggs () - having broken down the great table of tens logarithms. English Speidel compiled up to 1620 tables of natural numbers from 1 to London professor Edmund Tunter Vinish logarithmic scale, prototype of the logarithmic ruler.

Already in 1623, that is, 9 years after the first table was published, the English mathematician D. Gunter discovered the first slide rule, which became a working tool for many generations. Until the very next hour, when electronic computing technology is expanding everywhere before our eyes and the role of logarithms as a means of calculation is sharply decreasing.

The term "LOGARITHM" was coined by J. Napier; Vinik from the combination of the Greek words logos (here is a relation) and arithmos (number), which meant “number of wines”. The term “natural logarithm” belongs to M. Mercator. The daily meaning of the logarithm was first given by the English mathematician W. Gardiner (1742). The sign of the logarithm is the result of the abbreviation of the word “LOGARITHM”, which appears in various species almost immediately after the appearance of the first table [for example, Log in I. Kepler (1624) and G. Briggs (1631), log and B. Cavalieri (1632, 1643)]. Historical background

The first Russian logarithmic tables appeared in 1703. However, in all logarithmic tables there were allowances for the hour of calculation. The first non-military tables were published in 1857 in Berlin in a copy of the German mathematician K. Bremiker ()) 1. Kolmogorov A.N.. Algebra and the beginning of analysis. A handy tool for the class of dim lighting installations. M., “Osvita”, Algebra and analysis. Handbook for classes Edited by Sh.A. Alimov ta in. 11th type. M.: Enlightenment, List of Wikipedia Literature

Topic: UNDERSTANDING LOGARITHM. About the history of the development of logarithms. The word logarithm is similar to the combination of two walnut words (????? - “Word”, “Statement” and ??????? - “Number”) and is translated as a ratio of numbers, one of which is a member of the arithmetic progression, and another member of geometric progression. The first to understand this was the English mathematician John Napier, who was informed about this in a publication in 1614. In addition, this people know that the first one was the table of logarithms, which achieved great popularity among many years of history. The first tables of tens logarithms were compiled for 1617 rubles. English mathematician Briggs. The producers of logarithms did not create new logarithmic tables, even 9 years after their development in 1623. The first slide rule was created by the English mathematician Gunther. The Vaughn became a working tool for rich generations of engineers (until the 70s of the twentieth century). Nowadays, the meaning of logarithms can be found using a computer.

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Logarithm

"Fundamentals of the power of logarithms" - Types of logarithms. First tables of logarithms. John Napier. The power of logarithms. Biology Logarithmic tables. Chemistry and physical chemistry. Mechanics and physics. Theory of music. Logarithm and potency. History of the slide rule. Further development. Experiment. Schedule. Transition from one base to another.

“Logarithmic functions” - Two meanings are taken separately from the value of the basis. Concept of logarithm. The logarithm of the root is the same as the logarithm of the root expression and indicator of the root. Unraveling logarithmic unevenness. The logarithm of the stage is the same as the indicator of the stage on the logarithm of your sleep. The number is the boundary, which is a step with unbounded growth n.

“Understanding the logarithm” - The operation of calculating the logarithm is often called logarithm. Subject. The main principle is logarithmic identity. Ten logarithms to the output of calculators. Concept of logarithm. About the history of the development of logarithms. The jealousy is extremely graphic. Viznachennya. Step up. There will be two function graphs. Logarithm of the number b on the base.

“Vinahidnik logarithm” - Orpedelennya. Logarithms of their power. The main principle is logarithmic identity. Correctly vikonannya deyakih zavdan. The value of the logarithm can be written as follows: a log a b = b. Apply the Vikonannya to the deceitful commands. There are two gates at the steps. Were logarithms ever invented? The correct version of the butts.

“Natural logarithm” - a function of the form y=lnx, power and graph. Calculate the area of ​​the figure surrounded by the lines y=0, x=1, x=e and a hyperbola. Natural logarithms. Compare the graph of the function y=lnx at the point x=e. Tens of logarithms are much more convenient for our needs. "Logarithmic darts".

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Text instead of presentation slides: History of logarithms The term “logarithm” comes from the addition of the Greek words logos – ratio, relation and arithmos – number and is literally translated as a ratio of numbers. Logarithms were developed by the Scottish mathematician John Napier in the early 17th century. Napier John (1550 – 1617), Scottish mathematician, developer of logarithms. Neper is also the compiler of the first table of logarithms, which made the work of calculating the richest generations easier. The rise of logarithms influenced the development of mathematics. Continuous programs for showing and logarithmic functions in the most advanced fields of science and technology, and even invented logarithms to make calculations easier. More than three centuries have passed since the first logarithmic tables compiled by John Napier were published in 1614. They helped astronomers and engineers, speeding up the hour for calculations, and thus, as the famous French astronomer, mathematician and physicist Laplace said, “The cycle of logarithms, shortening the astronomer’s work, prolonged his life.” Slide rule (slide rule), a medical tool for simplifying calculations, in addition to which operations on numbers are replaced by operations on logarithms of these numbers. Intended for engineering and other applications. Until recently, it was important to spot an engineer without a logarithmic rule; which was discovered ten years after the appearance of logarithms. The same English mathematician Gunther. Vaughn made it possible to quickly remove the evidence with an accuracy of three digits sufficient for an engineer. Now microcalculators have come out of the engineering rig. But without a slide rule, early computers and microcalculators would not have been created. ...All sophisticated mysticisms are consumed by it. Isn't the musical din a set of advanced logarithms? The exponential function is also called the exponential function. Logarithms in the mystique We sang, as we did not assign them to exponents and logarithms, but guessed them in our verses. For example, Boris Slutsky sings at his top, having written the lines To him, that word is pena, Our rhymes will fall. Most of them seem to live up to this science. Nowadays, musicians talk about mathematics much more often, even though they themselves suspect, and even with such “terrible” speeches as logarithms. The famous physicist Eikhenwald said: “My comrade in the gymnasium loved to play the piano, but did not like mathematics. Well, speaking with a hint of ignorance, music and mathematics do not add up to anything meaningful. “It is true that Pythagoras knew the relationship between sound sounds, but Pythagoras itself turned out to be unpleasant for our music.” Let me know how unacceptable it is for my comrade, if I realize that while strumming the keys of my piano, I play, seemingly loudly, on logarithms...” , substitute those equal in two. A logarithmic spiral is a flat curve that is described by a point that falls in straight lines, which wraps around one of its points O (the poles of a logarithmic spiral) so that the logarithm of the point in The pole that collapses changes in proportion to the rotation; The logarithmic spiral moves under the constant line of the straight line that comes out of the pole. The shells of sea creatures can only grow in one direction. So that there is no need to twist into dovzhin, they have to twist, and the skin of the advancing turn is similar to the one in front. And this growth can also be achieved using a logarithmic spiral. Therefore, the shells of many mollusks, mollusks, and the very horns of such molluscs as argali (Girsky goats), are twisted in a logarithmic spiral. We can safely say that this spiral is a mathematical symbol for the growth form of growth. The great German singer, Johann Wolfgang Goethe, is a mathematical symbol of life and spiritual development. The outlines, curved in a logarithmic spiral, show not only the shells. In the dormouse, the seeds are spread out in arcs that are also close to a logarithmic spiral. One of the widest spiders, epeira, weaving webs, twists the threads around the center of a logarithmic spiral. There are a lot of galaxies swirling behind the logarithmic spirals, including the galaxy that lies within the Sonyachnaya system.

Logarithm

The history of logarithms and their stagnation

History of logarithms

Logarithms were introduced in the 16th century in connection with the need to carry out a great duty of calculations in the course of practical tasks, and first of all, the task of astronomy (from the standpoint of the position of courts behind the mirrors and the Sun). Logarithms were introduced by the Scottish mathematician John Napier (1550-1617) and the mathematician Jost Burgh (1552-1632). From the point of view of computational practice, the output of logarithms can safely be placed in order with the other, more long-standing great output of the Indians - our tenth. A dozen years after the appearance of logarithms in English, Gunther Vinaisov introduced a previously popular healing device - the slide rule. She helped astronomers and engineers with calculations, she made it possible to easily calculate three significant figures with sufficient accuracy. Now there were calculators, but without a slide rule there were no first computers, no microcalculators.

John Napier

Vinakhidnik of the first logarithmic tables, Neper, speaking about his sponkunaniya:

“I have been trying, for so long now, to try hard and tedious calculations, the tediousness of which is due to the richness of the learning of mathematics.”

Napier's partner, Brigg, who later became famous for finding tens of logarithms, wrote, having rejected Napier's work:

“With my new and marvelous logarithms, Neper Zmusiv was able to work with both my head and my hands. I’m tempted to make a mistake, because without ever reading a book, I would have liked it more and would have admired it.”

Brigg fulfilled his purpose and headed straight to Scotland to complete the logarithmic graph. At the hour, Brigg said:

“My lord, I have spent a lot of money on this in order to educate your person and learn about the help of some kind of instrument of reason and ingenuity. You have first come to the idea of ​​​​this miraculous manual for astronomers, and itself - logarithms; Well, my lord, after you knew them, I wonder why no one knew them before, so light the stench is given after you find out about them.”

Logarithms in the middle of nowhere

Logarithms are widely used in various fields of science:

Physics:

The intensity of sound (decibels) is also assessed by the same intensity on the decibel scale; number of decibels N=10lg(I/I0), where I is the intensity of the sound

Astronomy:

Once the visible brightness value is known and when you stand up to the object, you can calculate the absolute brightness value.

Chemistry:

The aqueous pH indicator is a measure of the activity of aqueous ions in water, which strongly expresses its acidity, calculated as the negative tenth logarithm of the concentration of aqueous ions, expressed in moles per liter .

From the music:

The basis of the control of the musical gams lies in the songs' regularities. To make it easier for you to figure out the logarithms of the subfrequencies, it appears.

In seismology:

When calculating the magnitude.

“FEEL TO THE UNHAPPY THIS DAY IS A YEAR IN WHICH YOU HAVE NOT CALLED ANYTHING NEW AND HAVE NOT ADDED ANYTHING TO YOUR COMPREHENSION.”

Y. A. KOMENSKY.

History of Logarithms

Development of the idea of ​​logarithms
One of the important ideas that underlies
output of logarithms
was already often seen by Archimedes
(3rd century BC),
were well known to N. Shuke (1484)
and to the German mathematician M. Stiefel (1544).
The stinks showed respect to those who multiplied and half the members of geometric progress
...a-3, a-2, a-1,1, a, a2, a3, ...
The folded and visible indicators that create arithmetic progression indicate
…-3, -2, -1,1, 0, 1, 2, 3,…

The Belgian mathematician Gregory of Saint-Vincent (1647) developed an important approach to the theoretical development of logarithms, which revealed the relationship of logarithms and areas surrounded by an arc of hyperbola, all abscists and types of ordinates ami.
The presentation of the logarithm by the unskewed series was given by M. Mercator (1668), who knew that
In(1+x) = x
Nezabar J. Gregory (1668) in a crooked layout
ln
This series converges very quickly, since M = N + 1 and N is very large; In this case, you can use the method for calculating logarithms.
The development of the theory of the logarithm has great significance
L. Euler.
They introduced the concept of logarithm as a factor, turning it into a step.
Development of the idea of ​​logarithms

Well, already in the middle of the 16th century. the basics of learning about logarithms were discussed. However, there were no clear, concrete methods for a broad practical understanding of these fundamentals in calculative mathematics, and there was no basis for understanding the idea of ​​logarithmic tables.
For example, XVI century. Simon Stevin published a table for calculating folding sums, the need for calculating such transactions was due to the growing number of trade and financial transactions.
Apparently, the formula for folding shirts is as follows:
A =a(1+(p/100))t
where a is the corn capital, A is the growth capital after t rocks at P%. Stevin’s table showed the values ​​of expressions (1+(p/100))t, and (p/100) =r Stevin also expressed in tens fractions: 0.04; 0.05; ..., as we are already in the wrong in Europe.
Stevin himself, astonishingly, did not note that tables can be used to simplify the calculations. Having learned this, however, one of his fellows - Byurgi
Development of the idea of ​​logarithms

Vinakhid logarithms
Vinakhid of logarithms on the cob of the 17th century. tightly knitted with a scroll in the 16th century. science and trade, astronomy and navigation, which required the improvement of the methods of calculative mathematics.
More and more often it is necessary to perform cumbersome operations on large-valued numbers, and the results of these actions become more and more precise.
This is where the idea of ​​logarithms was introduced, the value of which lies in the reduction of the complex actions of the third stage (reduced to a step and the development of the root) to the more simple ones of the second stage (multiplying and subdividing), and the remaining ones - to simplest, up to stage I ( Folding and lifting).

Vinakhid logarithms
Logarithms have quickly become practical. The discoverers of logarithms did not limit themselves to the development of a new theory. A practical feature was created - tables of logarithms, which dramatically increased the productivity of calculation workers.
The first tables of logarithms were compiled by the same Scottish mathematician J. Napier (1550 – 1617) and the Swiss I. Burgs (1552 – 1632). Napier's table, published in books under the titles "Description of the Dividing Table of Logarithms" (1614 rubles) and "Appendix of the Dividing Table of Logarithms" (1619 rubles), has increased the values ​​of logarithms of sines, cosines and tangs Ensіv for kutіv vіd 0 to 90 1 hvilin. The burghers prepared their tables of logarithms of numbers, perhaps, before 1610 rubles, but they began to light up the stench in 1620 rubles, even after Napier’s table was published, and thus became unmarked.

Vinakhid logarithms
Already in 1623, that is, 9 years after the first table was published, the English mathematician D. Gunter discovered the first slide rule, which became a working tool for many generations.
Until the very next hour, when electronic computing technology is expanding everywhere before our eyes and the role of logarithms as a means of calculation is sharply decreasing.

Historical background
The term "LOGARITHM" was coined by J. Napier; vin vinik with the addition of the walnut words logos (here - relation) and arithmos (number); in ancient mathematics, a square, cube, etc., lines a/b are called double, triple, etc. positions.
Thus, for Napier the words “logu arithmós” meant “number (multiplicity) of multiplicity”, while the logarithm of J. Napier is an additional number for vibrating the multiplicity of two numbers.
The term “natural logarithm” belongs to M. Mercator.
“Characteristics” – to the English mathematician G. Briggs
“Mantissa” in our rozumіnnі - logarithm - Euler
“Pіstava” to the logarithm – yomu
Understanding about the VV transition module
M. Mercator.
The daily meaning of the logarithm was first given by the English mathematician W. Gardiner (1742).
The sign of the logarithm - the result of the abbreviation of the word "LOGARITHM" - appears in various types immediately after the appearance of the first table [for example, Log - in I. Kepler (1624) and G. Briggs (1631), log and 1. - B. Cavalieri (1632, 1643)].

Portrait gallery
Scottish mathematician, scientist of logarithms.
Started at the University of Edinburgh. The main ideas about logarithms were discovered by Neper no later than 1594, in his “Description of the Dividing Table of Logarithms”, in which the price was stated, published in 1614.
This work included the meaning of the logarithm, explanations of its powers, tables of logarithms of sines, cosines, tangents and the definition of logarithms in spherical trigonometry.
In "The Wonderful Table of Logarithms" (published in 1619), Neper introduced the principle of calculating the table.
Napier John
(1550 - 1617)