Fokalne plohe

master's thesis

• Author: Ivo Šokčić
• Mentor: Željka Milin-Šipuš (mentor)
• Committee member: Željka Milin-Šipuš (predsjednik povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-06-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Fokalni skup plohe je skup svih njezinih središta zakrivljenosti. Općenito, (regularni) fokalni skup plohe može se sastojati od dvije plohe, takozvane fokalne plohe ili evolute, zatim od jedne plohe i jedne krivulje, ili od dvije krivulje. U radu su proučena diferencijalno-geometrijska svojstva tih skupova. Kada je riječ o fokalnom skupu jedne plohe i jedne krivulje, definirane su takozvane kanalne plohe, te detaljno obrađeni posebni slučajevi ovih ploha. Poseban oblik ploha gdje fokalni skup čine dvije krivulje su eliptičko-hiperboličke ciklide ili Dupinove ciklide, u čast francuskog matematičara koji ih je proučavao u devetnaestom stoljeću. U radu se navode sve potrebne definicije vezane uz fokalni skup. Sav teorijski materijal je popraćen konkretnim primjerima i slikama izrađenim koristeći programski paket "Wolfram Mathematica" [7].

Abstract (english)

The focal set of a surface is the locus of points of its centres of curvature. Generally, a (regular) focal set of surface may consist of two surfaces, so called focal surfaces or evolutes, then of one surface and one curve, or of two curves. In this thesis, differential geometric properties of the focal set are studied. In the special case, when the focal set consists of a surface and a curve, so called canal surfaces are defined. Also, their special classes are analysed: tubes and rotation surfaces. Finally, in the case when the focal set consists of two curve, we defined cyclides of Dupin of elliptic-hyperbolic type. They are named after the French mathematician Charles Dupin who studied them in the 19th century. This thesis presents all the definitions related to the focal set of a surface. All theoretical material is accompanied by concrete examples and figures made using the software package "Wolfram Mathematica" [7].

• Keywords: fokalne plohe; evolute; kanalne plohe; eliptičko-hiperboličke ciklide; Dupinove ciklide
• Keywords (english): focal set of a surface; evolutes; canal surfaces; elliptic-hyperbolic cyclides; cyclides of Dupin
• Language: croatian
• URN:NBN: urn:nbn:hr:217:628113
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-02-13 13:28:03