Ptolomejev teorem - dokazi, posljedice i poopćenja

master's thesis

• Author: Sanja Hršak
• Mentor: Mario Krnić (mentor)
• Committee member: Mario Krnić (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavamo Ptolomejev teorem i njegove inačice. Prvo, prikazujemo nekoliko različitih dokaza Ptolomejeva teorema. Nakon toga, pomoću Ptolomejeva teorema dokazujemo neke klasične teoreme iz elementarne geometrije, kao i nekoliko složenijih geometrijskih problema. Konačno, dajemo i nekoliko poopćenja Ptolomejeva teorema.

Abstract (english)

In this thesis we study Ptolemy's theorem and its variants. First we give several proof of Ptolemy's theorem. Then, we utilize the theorem for proving several classical theorems in elementary geometry. In addition, by virtue of Ptolemy's theorem we solve some complex geometric problems. Finally, we also study some generalizations of Ptolemy's theorem.

• Keywords: Ptolomejev teorem; geometrija; Bretschneiderova formula; Caseyjev teorem
• Keywords (english): Ptolemy's theorem; geometry; Bretschneider's formula; Casey's theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:425004
• 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: 2019-04-26 13:36:56