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Abstract

The basis of this chapter is the Euclidean algorithm, which has been part of mathematics since at least the fourth century BC, predating Archimedes. From the Euclidean algorithm we immediately obtain the expression of any rational number in the form of a finite continued fraction. A study of continued fractions shows us that they provide a more natural method of expressing any real number in terms of integers than the usual decimal expansion. An investigation of the “worst” case in applying the Euclidean algorithm leads to the Fibonacci sequence and so to other sequences generated by a linear recurrence relation.

Keywords

Recurrence Relation Continue Fraction Fibonacci Number Fibonacci Sequence Euclidean Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Piet Hein

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