## Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) – Uspenskii

In this post, we will see the book Some Applications Of Mechanics To Mathematics by V. A. Uspenskii. This book is Volume 3 of the Popular Lectures in Mathematics series. The applications of mathematics to physics (in particular, to mechanics) are well-known. We need only open a school text-book to find examples. The higher branches of mecha­nics demand a complex and refined mathematical apparatus.
There are, however, mathematical problems for whose solution we can successfully use the ideas and laws of physics. A number of problems of this kind soluble by methods drawn from mechanics (namely, by using the laws of equilibrium) were given by the author in his lecture “The solving of mathematical problems by the methods of mechanics”, which
was read to pupils in their seventh year of secondary school at the Moscow State University on 19 February 1956, this lecture, with very minor additions, makes up the contents of this article.

The book was translated from Russian by Halina Moss and edited by Ian N. Sneddon. was published in 1960.

You can get the book here.

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# Contents

Foreword vii

1. Problem on a tangent to a circle 1

2. Problem on a tangent to an ellipse 5

3. Problems on tangents to parabolas and hyperbolas 11

4. Principle of least potential energy 18

5. Material points and the centre of gravity 23

6. The centre of gravity and a system of two material points 28

7. Theorems about the intersection of straight lines 30

8. The centre of gravity of a rod with many loads 35

9. A problem in the theory of numbers (formulation) 39

10. A problem in the theory of numbers (solution) 43

11. The impossibility of perpetual motion 49

Conclusion 51 I am The Mitr, The Friend
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### 4 Responses to Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) – Uspenskii

1. manuel carames says:

there are 5 books. will we have access to the other 4?
thank you
manolo

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• The Mitr says:

There are not 5 but 19+ books in that series. We will see most of them soon.

Vol. 01 The Method of Mathematical Induction By I. S. Sominskii
Vol. 02 Fibonacci Numbers By N. N. Vorob’ev
Vol. 03 Some Applications of Mechanics to Mathematics By V. A. Uspenskii
Vol. 04 Geometrical Constructions using Compasses Only By A. N. Kostovskii
Vol. 05 The Ruler in Geometrical Constructions By A. S. Smogorzhevskii
Vol. 06 Inequalities By P. P. Korovkin
Vol. 07 One hundred problems in elementary mathematics By H. Steinhaus
Vol. 08 Complex Numbers and Conformal Mappings by A. Markushevich
Vol. 09 The Cube Made Interesting by Ehrenfeucht
Vol. 10 Mathematical Games and Pastimes by A. P. Domoryad
Vol. 11 A selection of problems in the theory of numbers by W. Sierpinski
Vol. 12 Mathematical Problems and Puzzles from the Polish Mathematical Olympiads by S. Straszewich
Vol. 13 Shortest paths: Variational problems by S. Straszewich
Vol. 14 Inversions by Ya. I Bakelman
Vol. 15 The Decomposition of Figures Into Smaller Parts by V. G. Boltyanskii
Vol. 16 Criteria for Divisibility by N. N. Vyoborev
Vol. 17 Systems of Linear Inequalities by A. S. Solodovnikov

Vol. ?? Number Systems by S. V. Fomin

Vol ?? Pascal’s Triangle V. A. Uspenskii

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2. tigerlasagnaminerva80732 says:

thank you very much!! this is GREAT!!

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