Novi pristup glasovitom problemu iz japanskog hrama Gion

master's thesis

• Author: Iva Leženić
• Mentor: Juraj Šiftar (mentor)
• Committee member: Juraj Šiftar (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Igor Ciganović (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-21, 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... More 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. Less

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... More 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. Less

• Keywords: Problem iz hrama Gion; japanski matematičar Ajima Naonobu; algebarska jednadžba stupnja 10
• Keywords (english): Gion Shrine Problem; Japanese mathematician Ajima Naonobu; algebraic equation of degree 10
• Language: croatian
• URN:NBN: urn:nbn:hr:217:812559
• 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: 2020-11-26 10:58:32