This thesis uses hyperbolic geometry to study various classes of both real and complex continued fractions. This intuitive approach gives insight into the theory of continued fractions that is not so easy to obtain from traditional algebraic methods. Using it, we provide a more extensive study of both Rosen continued fractions and even-integer continued fractions than many previous works, yielding new results, and revisiting classical theorems. We also study two types of complex continued fractions, namely Gaussian integer continued fractions and Bianchi continued fractions. As well as providing a more elegant and simple theory of continued fractions, our approach leads to a natural generalisation of continued fractions that has not been explored, before.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:700134 |
| Date | January 2016 |
| Creators | Walker, Mairi |
| Publisher | Open University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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