Continued Fractions

In this short book the first two chapters contain a very clear development of the theory of simple continued fractions, culminating in a proof of Lagrange's theorem on the periodicity of the continued fraction representation of quadratic surds. Chapter three presents Khinchins beautiful and original work on the measure theory of continued fractions. The proofs of the theorems in this chapter are also entirely elementary.


For Professionals   April 12, 2008
Lee P. Neuwirth (princeton, nj usa)
A wonderfully written, clear exposition of advanced material which, however, begins simply enough to lure one in.


Classic text, however not suitable for a first exposure.   October 6, 1999
71 out of 71 found this review helpful

This is Khinchin's classic work, translated from Russian in the 1930's. Although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times, the book moves at a truly alarming pace, and the book is not suitable to be used ALONE as an introduction to continued fractions. To supplement this book if this is a first exposure to continued fractions, I would recommend C.D. Old's book, which has many more examples which can be worked through until the reader is comfortable with the topic.

The book is brilliant and necessary for understanding continued fractions, but can't stand alone without supplemental material unless one is a professional mathematician. Khinchin frequently employs contrapositive proof formats, and there are occasional translation errors from Russian. The errors range from minor (awkward usage) to major (in one place, the translation is "negative" when it should be "non-negative", which confused me for half a day).


A good start!   October 4, 2005
Giorgio Ciociano (Italy)
5 out of 5 found this review helpful

You won't find many books on such an out-of-fashion theme as continued fractions, will you? Even less on the arithmetic side of the theory. Yes, it's true, many texts on elementary number theory provide a chapter or so about the subject, but if you want to gain a reasonably thorough picture of the field, without dwelling so much on details, you've got to resort to Kinchin's "Continued fractions": readable (no more mathematic needed than basics of analysis), complete (all fundamental conceptual aspects dealt with, included measure theory and implications on irrational numbers), brief (less than a hundred pages with virtually no applications - not even to Pell's equation!) and LIVELY in style.
All in all a very good start for understanding this profound mathematical tool.