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Master's Thesis
Author of thesis: Bc. Konstantin Kokh
Acad. year: 2025/2026
Supervisor: prof. RNDr. Miroslav Doupovec, CSc., dr. h. c.
Reviewer: prof. RNDr. Josef Mikeš, DrSc.
Plane curves are classical objects in geometry and arise naturally in many applications. They can be divided into two main groups: algebraic and transcendental curves. This thesis studies transcendental curves and compares them with algebraic ones. The main goal of the thesis is to present a structured overview of the most important representatives of transcendental curves. First, we recall basic tools from differential geometry, several methods for constructing curves, and selected characteristics of algebraic curves. Then we introduce transcendental curves and compare their properties with those of algebraic curves. The main part of the thesis is devoted to a collection of classical transcendental curves, including spirals, the catenary, the tractrix, the cycloid, the involute of a circle, and the clothoid. Although transcendental curves do not possess a general classification comparable to that of algebraic curves, they form a rich class with their own characteristic properties. The thesis shows that these curves are connected by recurring geometric constructions, natural equations, curvature properties, and applications in geometry, mechanics, and physics.
Plane curves, transcendental curves, algebraic curves, natural equation, curvature, special curves.
Date of defence
08.06.2026
Result of the defence
Defended (thesis was successfully defended)
Grading
B
Process of defence
Diplomant seznámil komisi s diplomovou prací. Oponent – prof. Mikeš – nebyl přítomen u obhajoby. Komise položila diplomantovi otázky k diplomové práci: Doc. Kureš položil dvě otázky: Jak se určí stupeň algebraické křivky. Jak můžeme z transcendentní parametrizace ověřit, zda je křivka algebraická nebo transcendentní. Student na otázky ne zcela uspokojivě odpověděl.
Language of thesis
English
Faculty
Fakulta strojního inženýrství
Department
Institute of Mathematics
Study programme
Mathematical Engineering (N-MAI-P)
Composition of Committee
doc. Mgr. Robert Mařík, Ph.D. (předseda) doc. RNDr. Miroslav Kureš, Ph.D. (místopředseda) doc. Ing. Jiří Šremr, Ph.D. (člen) doc. Ing. Pavel Štarha, Ph.D. (člen) doc. RNDr. Libor Žák, Ph.D. (člen)
Supervisor’s reportprof. RNDr. Miroslav Doupovec, CSc., dr. h. c.
Grade proposed by supervisor: B
Reviewer’s reportprof. RNDr. Josef Mikeš, DrSc.
Grade proposed by reviewer: B
Responsibility: Mgr. et Mgr. Hana Odstrčilová