Conway's topograph
| Thesis title in Czech: | Conwayův topograf |
|---|---|
| Thesis title in English: | Conway's topograph |
| Key words: | řetězové zlomky|cesty v grafu|topograf|Fareyho strom|lhostejné vektory |
| English key words: | continued fractions|paths in a graph|topograph|Farey tree|lax bases |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 03.04.2024 |
| Date of assignment: | 03.04.2024 |
| Confirmed by Study dept. on: | 03.04.2024 |
| Date of electronic submission: | 07.05.2024 |
| Opponents: | Nicolas Daans, Ph.D. |
| Guidelines |
| Conway's topograph is a certain graph containing all possible bases of Z^2 as edges; it nicely captures properties of binary quadratic forms and negative continued fractions. In the thesis, the student will carefully construct the topograph and establish its key properties. She will work our necessary facts about negative continued fractions and, time-permitting, establish the correspondence between certain paths in the topograph and these continued fractions. |
| References |
| J. H. Conway, The sensual (quadratic) form, Carus Mathematical Monographs, 1997
K. Spalding and A. P. Veselov, Growth of values of binary quadratic forms and Conway rivers, Bull. London Math. Soc. 50 (2018) 513–528 A. Hatcher, Topology of numbers, https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf |