Fascinating Fractions by N. M. Beskin (Little Mathematics Library).

This booklet is intended for high-school students interested in mathematics. It is concerned with approximating real numbers by rational ones, which is one of the most captivating topics in arithmetic.

    ...
Continued fractions represent one of the most perfect creations of 17-18th century mathematicians: Huygens, Euler, Lagrange, and Legendre. The properties of these fractions are really striking.

The following should be borne in mind when reading this
booklet. Topics easily understandable are presented in normal print,
while those more difficult are given in small print. Proofs of some theorems given in small print may be omitted safely. These theorems will necessarily be taken for granted. However, mathematics is not just reading for entertainment. A future mathematician as well as a physicist or an engineer has to acquire skill in dealing with  mathematical constructions and proofs. So take a pencil and a sheet of  paper and study carefully the topics given in small print. You may succeed in simplifying some proofs or finding better ones.



The book was translated from the Russian by V. I. Kisin and was first published by Mir Publishers in 1986.

DJVU | OCR | Bookmarked |  Cover | 827 KB | 88 pp

All credits to the original uploader.


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Contents

Preface 7

Chapter 1. Two Historical Puzzles

Chapter 2. Formation of Continued Fractions

Chapter 3. Convergents

Chapter 4. Nonterminating Continued Fractions

Chapter 5. Approximation of Real Numbers

Chapter 6. Solutions

Bibliography 88