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Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3)  V. A. Uspenskii
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Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3)  

Original Title  Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) 
Author  V. A. Uspenskii 
Publication date 
1961 
Topics  mathematics, soviet, popular lectures, tangents, applications. mechanics, theory of numbers, potential energy, centre of gravity, perpetual motion, quadric curves, material points 
Collection  mirtitles, additional_collections 
Book Type  EBook 
Material Type  Book 
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FOREWORD
The applications of mathematics to physics (in particular, to mechanics) are wellknown. We need only open a school textbook to find examples. The higher branches of mecha nics demand a complex and refined mathematical apparatus.
There are, however, mathematical problems for whose solu tion 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.
Foreword vii
1. Problem on a tangent toa 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

Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3)
 V. A. Uspenskii
Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) Orig
Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3)
 V. A. Uspenskii
Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) Orig