Vybrané úlohy z diferenciální geometrie
| Thesis title in Czech: | Vybrané úlohy z diferenciální geometrie |
|---|---|
| Thesis title in English: | Selected problems in differential geometry |
| Key words: | rovnoběžné křivky|trochoidy|Mamikonova věta|planimetr |
| English key words: | parallel curves|trochoids|Mamikon's theorem|planimeter |
| Academic year of topic announcement: | 2019/2020 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Mathematics Education (32-KDM) |
| Supervisor: | doc. RNDr. Antonín Slavík, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 30.04.2020 |
| Date of assignment: | 13.05.2020 |
| Confirmed by Study dept. on: | 22.05.2020 |
| Date and time of defence: | 16.06.2022 08:30 |
| Date of electronic submission: | 02.05.2022 |
| Date of submission of printed version: | 05.05.2022 |
| Date of proceeded defence: | 16.06.2022 |
| Opponents: | doc. RNDr. Zbyněk Šír, Ph.D. |
| Guidelines |
| Obsahem práce budou různá témata volně navazující na úvodní přednášku z diferenciální geometrie. Důraz bude kladen na rovinné křivky, evoluty, evolventy, výpočet obsahů rovinných oblastí a příbuzná témata. Příslušná teorie bude ilustrována na příkladech. |
| References |
| - Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces, Prentice Hall, 1976
- John Bryant, Chris Sangwin: How Round Is Your Circle?, Princeton University Press, 2008 - Dmitry Fuchs, Serge Tabachnikov: Mathematical Omnibus. Thirty Lectures on Classic Mathematics, American Mathematical Society, 2007 - Tom M. Apostol, Mamikon A. Mnatsakanian: Subtangents - An Aid to Visual Calculus, American Mathematical Monthly 109 (2002), 525-533 - Tom M. Apostol, Mamikon A. Mnatsakanian: Tanvolutes: Generalized Involutes, American Mathematical Monthly 117 (2010), 701-713 - Leon Hall, Stan Wagon: Roads and Wheels, Mathematics Magazine 65 (1992), 283-301 - Michael E. Hoffman: The Bull and the Silo: An Application of Curvature, American Mathematical Monthly 105 (1998), 55-58 - Stan Wagon: The Ultimate Flat Tire, Math Horizons 6 (1999), 14-17 |