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Development of experimental sets for a new conception of Optics in the Interactive Physics Laboratory II
Ceháková, Lydia ; Snětinová, Marie (advisor) ; Drozd, Zdeněk (referee)
In this thesis, a new experimental set for the Interactive Physical Laboratory (IPL), operated by the Faculty of Mathematics and Physics, Charles University, was designed. This experimental set consists of five units named: Measurement of Refractive Index, Malus's Law, Diffraction of Light on Grating, Polarization of Light, Young's Experiment. Most of the units consist of quantitative physics experiments in wave and geometrical optics, inspired by experiments appearing in Czech resources. For each unit, corresponding worksheets were prepared and tested. The worksheets are supposed to guide the students as they go through the experiments and related tasks. Each unit is described in the thesis including typical mistakes students tend to make and methodology for lecturers of the laboratory. The author's solution is included in attachments. A part of the thesis is also dedicated to the introduction of the necessary physics theory that could be used as a study material for visitors of the laboratory.
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Space-filling curves
Ceháková, Lydia ; Rmoutil, Martin (advisor) ; Staněk, Jakub (referee)
The first part of this thesis deals with Cantor's bijection and the historical develop- ment of the notion of curve. Here, the proof of existence of Cantor's bijection is introduced and it is followed by a discussion of the importance of this bijection for further advance- ment of mathematics and the theme of space-filling curves. The section about historical development of curves explores different approaches to the definition and its changing interpretation through time, from the Ancient Greece up until the 20th century. The second part of the thesis introduces the issue of space-filling curves. The segment descri- bes different methods of space-filling curves construction, particularly the geometric and the arithmetic construction of the Hilbert and the Peano Curve, as these were the first examples of the said curve. Furthermore, typical properties of the space-filling curves are discussed, explained and proofed with special attention dedicated to their nowhere diffe- rentiability. There are also some additional examples of 2D space-filling curves - including the Sierpiński Curve - and some 3D variations of some of them. The illustrative figures presented throughout the text are also a crucial component of the thesis. 1
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