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master's thesis
Euklidska, hiperbolička i sferna trigonometrija
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:572876
Kavčić, Iva
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kavčić, I. (2018). Euklidska, hiperbolička i sferna trigonometrija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:572876

Kavčić, Iva. "Euklidska, hiperbolička i sferna trigonometrija." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:572876

Kavčić, Iva. "Euklidska, hiperbolička i sferna trigonometrija." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:572876

Kavčić, I. (2018). 'Euklidska, hiperbolička i sferna trigonometrija', Master's thesis, University of Zagreb, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:572876

Kavčić I. Euklidska, hiperbolička i sferna trigonometrija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:572876

I. Kavčić, "Euklidska, hiperbolička i sferna trigonometrija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:572876

Metadata
TitleEuklidska, hiperbolička i sferna trigonometrija
AuthorIva Kavčić
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberHrvoje Šikić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-03-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog diplomskog rada je dokazati osnovne relacije između mjera kutova i duljina stranica trokuta u euklidskoj i hiperboličkoj ravnini te na površini sfere. Rad započinje povijesnim pregledom razvoja trigonometrije, od samih početaka u 18. st. pr. Kr. kad se razvila iz praktičnih potreba vezanih za graditeljstvo, astronomiju i navigaciju do danas kad je to zasebna matematička disciplina. Slijede definicije i svojstva trigonometrijskih funkcija sinus, kosinus, tangens i kotangens te njihovih inverznih funkcija. Potom proučavamo sličnosti i razlike između trigonometrijskih relacija u tri različita modela: modelu euklidske ravnine, modelu hiperboličke ravnine te modelu sfere. Svaki od modela najprije definiramo i iskazujemo svojstva istog, zatim promatramo trigonometriju u modelu. Naposljetku dolazi neutralni sinusov teorem koji vrijedi u svakom od promatranih modela.
Abstract (english)
The aim of this graduate thesis is to prove basic relations between angle measures and edge lengths of a triangle in Euclidean plane, hyperbolic plane and on the surface of the sphere. The thesis begins with a historical overview of trigonometry, from the very beginnings in the 18th century BC when it developed from practical needs and was used in engineering distinct, astronomy and navigation, until today when it is a mathematical discipline. Next are definitions and properties of trigonometric functions sine, cosine, tangent, cotangent and their inverse functions. Thereafter, we analyzed similarities and differences between trigonometric relationships in three different models: the Euclidean plane model, the hyperbolic plane model and the sphere model. Firstly we defined each model, declared properties and then we analyzed trigonometry of it. Finally, we state the neutral law of sines which is valid in each of the models.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:572876
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-08-31 12:27:16