Cikloidne krivulje

master's thesis

• Author: Valentina Pekić
• Mentor: Željka Milin Šipuš (mentor)
• Committee member: Željka Milin Šipuš (predsjednik povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Committee member: Franka Miriam Bruckler (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Chemistry

Abstract

Tema ovog diplomskog rada su cikloidne krivulje. Cilj rada je jednadžbama i grafički prikazati neke od cikloidnih krivulja. Za vizualizaciju grafičkih prikaza korišten je program dinamičke geometrije GeoGebra. U prvom poglavlju prikazana je kratka povijest razvoja cikloidnih krivulja te njihove znamenitosti. Izvedene su jednadžbe i opisana neka svojstva koja vrijede. Glavni dio rada predstavljen je u drugom i trećem poglavlju. Glavni dio je posvećen proučavanju prostornih krivulja koje leže na sferi, a čijom projekcijom na \(xy\) ravninu dobivamo neku od cikloidnih krivulja. Također je proveden istraživački dio rada ispitivanja postoje li prostorne krivulje na nekoj drugoj kvadrici čijom projekcijom bismo mogli dobiti cikloidnu krivulju. Na taj način dolazimo do krivulja koje leže na hiperboloidu, a u projekciji dobivamo pseudo-krivulje.

Abstract (english)

The subject of this master thesis are cycloid curves. The main goal is to show some of the curves graphically and with equations. Visualisation of graphs is done in tool of dynamic geometry called GeoGebra. The first chapter brings short history of cycloid curves and their importance. Equations are presented and some attributes are described. The main part of the thesis is shown in second and third chapter. The main part is devoted to the study of space curves on a sphere, whose projection on a \(xy\) plane are cycloid curves. Furthermore, research part of the thesis deals with space curves on another quadric whose projection is a cycloid curve. In that way, we get to the curves on hyperboloid, and in projection we get pseudo curves.

• Keywords: cikloidne krivulje; GeoGebra; pseudo-krivulje
• Keywords (english): cycloid curves; GeoGebra; pseudo curves
• Language: croatian
• URN:NBN: urn:nbn:hr:217:362190
• 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: Open access
• Created on: 2020-02-17 11:07:52