Continued fractions with irrational numerators

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Continued fractions with irrational numerators

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A continued fraction is called a simple continued fraction when the numerator is 1 and non-simple otherwise. Simple continued fractions of square roots have particularly "nice" periodic patterns. For example, sqrt{19} = [4,{2, 1, 3, 1, 2, 8}]_1 where the sequence 2, 1, 3, 1, 2, 8 is the periodic part which repeats. The pattern is "nice" because the first term is always half the last terms and the sequence 2, 1, 3, 1, 2 is identical when reversed. In this report, we study the periodic behavior of non-simple continued fractions of general square root with square root numerators. We show that these have many similarities to simple continued fraction expansions of square roots.


University of Minnesota M.S. thesis. June 2018. Major: Applied and Computational Mathematics. Advisor: John Greene. 1 computer file (PDF); iii, 43 pages.

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Thalagoda, Kalani. (2018). Continued fractions with irrational numerators. Retrieved from the University Digital Conservancy,

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