C. Kimberling, A visual Euclidean algorithm in Mathematics Teacher, vol 76 (1983) pages 108-109. is the earliest reference I have found to the Rectangle Jigsaw approach to continued fractions. ^^ Introduction to Number Theory with Computing by R B J T Allenby and E Redfern 1989, Edward Arnold publishers, ISBN: 0713136618
is an excellent book on continued fractions and lots of other related and interesting things to do with numbers and suggestions for programming exercises and explorations using your computer. ^^ The Higher Arithmetic by Harold Davenport,
Cambridge University Press, (7th edition) 1999, ISBN: 0521422272
is an enjoyable and readable book about Number Theory which has an excellent chapter on Continued Fractions and proves some of the results we have found above. (More information and you can order it online via the title-link.)
Beware though! We have used [a,b,c,d,...]=X/Y as our concise notation for a continued fraction but Davenport uses [a,b,c,d,..] to mean the numerator only, that is, just the X part of the (ordinary) fraction! ^^ Introduction to the Theory of numbers by G H Hardy and E M Wright Oxford University Press, 1980, ISBN: 0198531710
is a classic but definitely at mathematics undergraduate level. It takes the reader through some of the fundamental results on continued fractions. Surprisingly, it doesn't have an Index, but there is a Web page Index to editions 4 and 5 that you may find useful. ^ Continued Fractions by A Y Khinchin, ISBN: 0 486 69630 8
This is a Dover book (Sept 1997), well produced, slim and cheap, but it is quite formal and abstract, so probably only of interest to serious mathematicians!
^^ A Limited Arithmetic on Simple Continued Fractions, C T Long and J H Jordan, Fibonacci Quarterly, Vol 5, 1967, pp 113-128;
^^^ A Limited Arithmetic on Simple Continued Fractions - II, C T Long and J H Jordan, Fibonacci Quarterly, Vol 8, 1970, pp 135-157;
^^ A Limited Arithmetic on Simple Continued Fractions - III, C T Long, Fibonacci Quarterly, Vol 19, 1981, pp 163-175;
Three articles on continued fractions with a single repeated digit or a pair of repeated digits or with a single different digit followed by these patterns.
1-61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More..
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©1996-2001 Dr Ron Knott [email protected] last update:13 April 2001
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