Visualization of knots with Mathematical computation
| Autor: | 張鳳蘭 |
|---|---|
| Rok vydání: | 2012 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 100 The paper is the research of knots with the use of Mathematical software. Firstly, we introduce two-dimensional curves such as Lissajous figures, cycloids, and trochoids. Then, we extend to the three- dimensional knots such as Lissajous knots, trochoid knots, torus knots, and the decorative knots. In the study of Lissajous knots, we have a series of analysis between the different phases and frequencies. For the trochoid knots and the torus knots, we focus on the affection of the various coefficients in the formulas to the knot patterns. We also try to have the formulas varied in order to result in the special shape of knots. Besides, there is a heavy discussion about SU(2). Furthermore, we can generate the SU(2) knots using the idea of SU(2) transformations combined with the 3D knot generating formula. Finally, we introduce the musical theory about scales for the goal of designing knot notes. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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