The algebra and geometry of using continued fractions for approximating real and complex numbers
| dc.contributor.author | Mennen, Carminda Margaretha | |
| dc.date.accessioned | 2023-11-23T08:22:28Z | |
| dc.date.available | 2023-11-23T08:22:28Z | |
| dc.date.issued | 2022 | |
| dc.description | A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, University of the Witwatersrand, 2022 | |
| dc.description.abstract | Through geometric analysis we forge a new interpretation of the link between nearest integer continued fractions and the Farey tessellation of hyperbolic space. Instead of just truncating the continued fraction to generate approximations, we focus on • how to parse the product of maps derived from the nearest integer continued fraction into a product of parabolic and elliptic Mobius maps and ¨ • on the collection of points on which these maps act. It turns out that we need to set apart the elliptic maps that permute a collection of six vertices, three values in R, namely ∞, 0 and 1, and three values in C, namely i, 1 + i and 1+i 2 . The action of the remaining parabolic maps on the same six vertices results in the creation of a sequence of nested Farey quadrilaterals, containing the target, whose boundaries are based in the Schmidt arrangement formed by the Farey sets and dual Farey sets of Schmidt. | |
| dc.description.librarian | PC(2023) | |
| dc.faculty | Faculty of Science | |
| dc.identifier.uri | https://hdl.handle.net/10539/37142 | |
| dc.language.iso | en | |
| dc.phd.title | PhD | |
| dc.school | Mathematics | |
| dc.subject | Algebra and Geometry | |
| dc.subject | Continued Fractions | |
| dc.subject | Approximating real and complex numbers | |
| dc.title | The algebra and geometry of using continued fractions for approximating real and complex numbers | |
| dc.type | Thesis |