Geometrija kugle i sfere

master's thesis

• Author: Ružica Korać
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučavamo osnove geometrije kugle i sfere. Prvo poglavlje analizira kuglu i njene dijelove, te njihove volumene. U drugom poglavlju bavimo se sferom i površinom sfere i njenih dijelova, presjecima sfere i ravnine, te svojstvima kružnica koje se dobivaju tim presjecima. Određujemo sferu sa četiri nekomplanarne točke. Treći dio govori o sfernim koordinatama, gdje uvodimo Jacobijevu matricu i pokazujemo kako doći do volumena kugle i nekih njenih dijelova koristeći sferni koordinatni sustav. Posljednje, četvrto poglavlje, daje kratki pregled sferne geometrije, gdje se upoznajemo sa sfernim i polarnim trokutima.

Abstract (english)

In the first chapter we analyze the globe and its parts, and their volume. In the second chapter we deal with the sphere and the surface area of the sphere and its parts, intersections between spheres and planes, and properties of circles that are obtained at intersections. We determine the sphere with four point that do not lie in the same plane. The third part talks about the spherical coordinates, where we introduce the Jacobian matrix and show how to find the volume of a globe and its parts using a spherical coordinate system. Lastly, the fourth chapter gives a brief overview of spherical geometry, where we meet spherical and polar triangles.

• Keywords: geometrija kugle; geometrija sfere; sferne koordinate; Jacobijeva matrica; sferni trokuti; polarni trokuti
• Keywords (english): globe; sphere; sperical coordinates; Jacobian matrix; spherical geometry; spherical triangles; polar triangles
• Language: croatian
• URN:NBN: urn:nbn:hr:217:698774
• 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: 2019-02-14 12:41:22