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SERIOUSLY
POPULAR
In this article we publish a solution to books that are of interest to the reader of our magazine.
In the future, our field of vision will include educational literature, books generally classified as “popular,” and other publications. Of course, this “classification” is more than arbitrary, but we are interested in one thing—that all these books be accessible and interesting to a wide range of our readers.
This review is dedicated to a group of books published under the general title “Popular Lectures”*). There are currently 48 issues in this series.
The authors of issues in this series, as a rule, are well-known mathematicians, and the topics covered in the issue generally coincide with the area of scientific interests.
The books in this series are called lectures. This is not accidental—most of the issues are written on the basis of lectures that the author once gave to schoolchildren.
The series is called popular. A popular book is not necessarily an entertaining book or a book for easy reading. Science does not need ornamentation; it is attractive in itself. Therefore, any of the issues of “Popular Lectures” is traditionally intended for server reading,
*) Published by the Main Editorial Board of Physics and Mathematics Literature of the Nauka Publishing House.
to work with the book. It is popular, that is, it is simple and accessible to those high school students who have the desire, patience, and time to engage in mathematical self-education. Percett is such a high-class book from this series one, two, three times, as many as he needs, and the identity of the author begins to appear through the text. You just need to read with a gain similar to that needed when solving mathematical problems.
Some issues of the series “Popular Lectures on Mathematics”, which were met with particular interest, have been published several times in the years that have passed since the first of them was published. In particular, of the books presented here, S.V. Fomin’s book “Number Systems” is published for the second time, N.N. Vorbeva’s “Fibonacci Numbers” is published for the third time, and Ya.S.Dubnova’s “Errors in Geometric Proofs” is published even for the fourth time.
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Everything indicates that the authors of books try to assimilate them as much as possible during reprints. As a rule, this means that the author tries to further saturate each book with scientific information, leaving it no less accessible.
With this we can consider that our first acquaintance with the serial book “Popular Lectures on Mathematics” consists. Let us now get acquainted, so to speak, personally with five books that were published in 1969-70, the covers of which are depicted here. Each of them has its own individual characteristics.
Let’s start with the book:
N. N. Vorobyov. “Fibonacci numbers”. 112 pages. Price 17 kopecks.
Elementary mathematics is rich in developmental tasks and puzzles that turn out to be closely related to each other. Forming new connections after small and large open mathematicians, this complex formation imperceptibly turns into a serious mathematical theory. This is exactly what was done with the problem of the Intayan mathematician Leonardo of Pisa on the origin of Fibonacci, published by him for the first time in 1202. Growing out of the famous “rabbit problem”, which is more than seven hundred and fifty years old, the theory of Fibonacci numbers remains one of the most fascinating chapters of elementary mathematics. Moreover, this ancient problem turned out to be “closely related” not only to such a science as number theory, but even to the very young theory of the concept of optimal solution.
And at first the task read like this:
How many pairs of rabbits does one pair give away in one year?
《Someone placed a pair of rabbits in a certain place, surrounded on all sides by a wall, to find out how many pairs of rabbits would be born during the year, if the nature of rabbits is such that after a month a pair of rabbits gives birth to another pair, and rabbits are born from the second place after their birth…》
How this problem is solved and what mathematical consequences it leads to, you will learn by reading this book.
The book is fully accessible to schoolchildren in grades 8-10.
By applying several conditions, you will have the opportunity to get acquainted with the reflection of mathematics, the application of which in practice promises a great future for it. Each of the reincarnations of Fibonacci problems is bright in itself.
Now about the next book:
S. V. Fomin. “Number systems”. 48 pages. Price 7 kopecks.
It is extremely easy to read. However, the ease of presentation did not allow the author to tell in a completely sincere and very interesting way everything necessary to create in the reader an idea of the number system.
First, it talks about the applications of the decimal system, to which the reader has become accustomed during his time at school, and therefore is inclined to accept these applications as they should. Then it talks about
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the advantages of other number systems in some interesting problem situations. In connection with the double number system, the author presents basic information about computers. However, we will not retell the contents of the book - it is a very interesting read. We will limit ourselves to the fact that it will also be useful to you if you want to get acquainted with the principles of operation of electronic computing devices.
Let’s move on to the book:
Y. S. Dubnov. “Errors in geometric proofs”.
64 pages. Price 9 kopecks.
Ya. S. Dubnov’s book contains a number of erroneous proofs and data analysis. In one problem, an error in the proof emerges, in others, both the inconsistency of the proof and the fallacy of statements. It is very possible that you will not be able to open yourself to it after you become acquainted with the proof of the theorem “All triangles are isosceles”, given on pages 14-16.
The book is written in clear, engaging language. It contains subtle and elegant geometric sophistry. It is quite accessible even to 7th grade students.
Let’s open the book now:
A. S. Solodov and Co. “System of linear inequalities”.
80 pages. Price 11 kopecks.
This brochure, gradually introducing new concepts and ideas for the student, leads him to reflect the successful research of scientists just some twenty to thirty years ago. We are talking about linear programming. And linear programming, as you may know, is closely related to the solution of many
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hy practical problems of mathematical economics.
The book by A. S. Solodovnikov is characterized by an emphasis exclusively on the mathematical content of linear programming. This makes it especially interesting for those students who are more interested in mathematics than economics.
After you understand this book, it will serve as a place for the back-end scientific works listed in the bibliography for it. And this will be a step into great science.
Finally, about the book by L. A. Kaluzhin and N. “The Fundamental Theorem of Arithmetic”. 32 pages. Price 5 kopecks.
This brochure is devoted to one of the main principles of the arithmetic of rational integers - the unique decomposition of integers into simple components. It provides a rigorous and complete proof of this basic fact.
This is how the basic theorem of arithmetic is formulated in the brochure: