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master's thesis
Novi pristup glasovitom problemu iz japanskog hrama Gion
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:812559
Leženić, Iva
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Leženić, I. (2020). Novi pristup glasovitom problemu iz japanskog hrama Gion (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:812559

Leženić, Iva. "Novi pristup glasovitom problemu iz japanskog hrama Gion." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:812559

Leženić, Iva. "Novi pristup glasovitom problemu iz japanskog hrama Gion." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:812559

Leženić, I. (2020). 'Novi pristup glasovitom problemu iz japanskog hrama Gion', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:812559

Leženić I. Novi pristup glasovitom problemu iz japanskog hrama Gion [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:812559

I. Leženić, "Novi pristup glasovitom problemu iz japanskog hrama Gion", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:812559

Metadata
TitleNovi pristup glasovitom problemu iz japanskog hrama Gion
AuthorIva Leženić
MentorJuraj Šiftar (mentor)
Committee memberJuraj Šiftar (predsjednik povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberRudi Mrazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-07-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Iz japanske tradicije postavljanja sangaku-a u svetištima i hramovima proiziašli su mnogi zanimljivi problemi, od kojih je jedan, takozvani Problem iz hrama Gion. Iako se japanski matematičar Ajima Naonobu još 1774: godine pročuo rješenjem u kojem je složeni geometrijski zadatak sveo na rješavanje algebarske jednadžbe stupnja 10, tek je u 21: stoljeću objavljeno sažetije rješenje i temeljita analiza postojanja rješenja. U ovom radu prikazano je to rješenje, a postupak rješavanja je sistematiziran i detaljno objašnjen. Određeno je područje vrijednosti parametra u skupu realnih brojeva za koje je problem rješiv, a rješenje je tada jedinstveno. Ponovno ključnu ulogu ima polinom 10: stupnja, ali njegov je zapis ovaj put značajno jednostavniji, zahvaljujući povoljnijem izboru varijable, dobivene slijedom sup stitucija proizašlih iz trigonometrijskih relacija.
Abstract (english)
Japanese tradition of hanging Sangaku in temples and shrines resulted in many interesting problems, one of which is, so called, Gion Shrine Problem. Although a Japanese mathematician Ajima Naonobu was famed in 1774 for deriving a solution in which he reduced a complex geometric problem to that of solving an algebraic equation of degree 10, it was only in 21st century that it was published a concise and more thorough analysis of existence of solutions. That solution is presented in this paper and the entire solution process is systemized and explained in detail. A domain, in which a parameter is defined in the reals and for which the problem is solvable, is specified. It then follows that a solution is unique. A crucial role plays again a polynomial of degree 10, but this time with a significantly simpler notation, thanks to a much more favorable choice of variable obtained from a sequence of supstitutions regarding trigonometric relations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:812559
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 on2020-11-26 10:58:32