Abstract
The connection between Euclid's algorithm and continued fractions is given in a fashion that allows easy generalization to higher dimensions. We explore this generalization which yields Jacobi's algorithm and two‐dimensional continued fractions. In addition, the computer science problem of efficient computation of Euclid's or Jacobi's algorithm is solved by generalizing a technique of D. H. Lehmer. Also, some open problems are mentioned for Jacobi's algorithm.
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