Konike u ravninskoj diferencijalnoj geometriji

master's thesis

• Title (english): Conics in plane differential geometry
• Author: Hrvoje Petrinić
• Mentor: Željka Milin Šipuš (mentor)
• Committee member: Željka Milin Šipuš (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-07-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog diplomskog rada bio je opisati sve tri konike u diferencijalnoj geometriji koristeći definicije i teoreme obrađene na kolegiju Uvod u diferencijalnu geometriju. U prvom poglavlju rada detaljno su obrađena osnovna svojstva konika koja se obrađuju u srednjoj školi. U drugom poglavlju susrećemo se s fakultetskim pojmovima kao što je zakrivljenost krivulje koju opisujemo raznim formulama iz diferencijalne geometrije. Konstrukcije su obrađene u matematičkog programu GeoGebra. Od konstrukcija najvažnije su bile konstrukcije oskulacijskih kružnica konika i njihovih evoluta. Koristeći se parametrizacijom krivulje, izveli smo i parametrizaciju njihovih evoluta. Konike imaju široku primjenu u građevini i arhitekturi, ali i u svakodnevnim aktivnostima stoga ih je poželjno proučavati.

Abstract (english)

The aim of this thesis was to describe all three conics in differential geometry using the definitions and theorems processed in the course Introduction to Differential Geometry. In the first chapter, the basic properties of conics, which are studied in high school, are covered in detail. In the second chapter we meet terms from college such as the curvature of a curve, which we describe with various formulas from differential geometry. The constructions were processed in the mathematical program GeoGebra. Of the constructions, the most important were the constructions of the osculation circles of conics and their evolutes. Using the parametrization of the curve, we also derived the parametrization of their evolutes. Conics are widely used in construction and architecture, but also in everyday activities, so it is desirable to study them.

• Keywords: zakrivljenost krivulje; GeoGebra; konstrukcije oskulacijskih kružnica konika
• Language: croatian
• URN:NBN: urn:nbn:hr:217:222727
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-07-24 12:50:54