prikaz prve stranice dokumenta Tetivno-tangencijalni četverokut
  Download
PDF 1.52 MB
master's thesis
Tetivno-tangencijalni četverokut
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:229019
Mesić, Kevin
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mesić, K. (2023). Tetivno-tangencijalni četverokut (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:229019

Mesić, Kevin. "Tetivno-tangencijalni četverokut." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:229019

Mesić, Kevin. "Tetivno-tangencijalni četverokut." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:229019

Mesić, K. (2023). 'Tetivno-tangencijalni četverokut', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:229019

Mesić K. Tetivno-tangencijalni četverokut [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:229019

K. Mesić, "Tetivno-tangencijalni četverokut", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:229019

Metadata
TitleTetivno-tangencijalni četverokut
Title (english)Bicentric quadrilateral
AuthorKevin Mesić
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
Committee memberAna Prlić (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu upoznali smo se s pojmom tetivno-tangencijalnog četverokuta te nekim njegovim značajnim svojstvima i karakterizacijama. Rad je podijeljen u dva poglavlja. U prvom poglavlju dokazujemo svojstva tetivnih i tangencijalnih četverokuta koja nam služe za dokazivanje karakterizacija tetivno-tangencijalnog četverokuta. U drugom poglavlju definiramo tetivno-tangencijalni četverokut te pokazujemo neke njegove karakterizacije. Nadalje, promatramo odnos Newtonovog pravca tetivno-tangencijalnog četverokuta i Newtonovog pravca njemu kontaktnog četverokuta, dokazujemo Fussov teorem koji pokazuje odnos između radijusa upisane i opisane kružnice tetivno-tangencijalnog četverokuta, Ponceletovu propoziciju te Carlitzovu nejednakost. Zatim dokazujemo Yunovu nejednakost za tetivno-tangencijalne četverokute. U dodatku rada definiramo i pokazujemo osnovna svojstva potencije točke s obzirom na kružnicu i inverzije.
Abstract (english)
In this thesis, we were introduced to the concept of bicentric quadrilateral and some of its significant properties and characterizations. The work is divided into two chapters. In the first chapter, we prove the properties of cyclic and tangential quadrilaterals, which will serve us to prove the characterizations of bicentric quadrilaterals. In the second chapter, we define the bicentric quadrilateral and show some of its characterizations. Furthermore, we observe the relationship between Newton’s line of the bicentric quadrilateral and Newton’s line of its contact quadrilateral, we prove Fuss’s theorem that shows the relationship between the radius of the inscribed and the radius of the circumscribed circle of the bicentric quadrilateral, Poncelet’s proposition and Carlitz’s inequality. Then we prove Yun’s inequality for bicentric quadrilaterals. In the appendix of this thesis, we define and show the basic properties of the power of a point with respect to the circle and inversion
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:229019
Study programmeTitle: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education
Course: Mathematics and Computer Science Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-08-18 06:36:24