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master's thesis
Neki stari japanski teoremi o elipsama
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:207272
Marinov, Marko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Marinov, M. (2017). Neki stari japanski teoremi o elipsama (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:207272

Marinov, Marko. "Neki stari japanski teoremi o elipsama." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:207272

Marinov, Marko. "Neki stari japanski teoremi o elipsama." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:207272

Marinov, M. (2017). 'Neki stari japanski teoremi o elipsama', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:207272

Marinov M. Neki stari japanski teoremi o elipsama [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:207272

M. Marinov, "Neki stari japanski teoremi o elipsama", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:207272

Metadata
TitleNeki stari japanski teoremi o elipsama
AuthorMarko Marinov
MentorJuraj Šiftar (mentor)
Committee memberJuraj Šiftar (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberOzren Perše (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-07-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Japanska tradicija postavljanja matematičkih problema na drvenim pločicama zvanima sangaku, koje su izlagane u svetištima i hramovima, naročito se razvijala u razdoblju od 17. do 19. stoljeća. Iz tih izvora proizašli su mnogi zanimljivi i katkad vrlo teški problemi, većinom geometrijski, koji se pritom odlikuju specifičnim stilom. U ovom radu prikazani su suvremeni dokazi nekih rezultata objavljenih u Japanu u 19. stoljeću, koji govore o posebnim međusobnim položajima elipsi i drugih konika te još nekih geometrijskih likova. Dokazi određenih teorema (Terao) i izvodi formula (Shiraishi) pritom su povezani te izloženi sažeto i precizno, primjenom linearne algebre, analitičke geometrije, kao i prikladnih geometrijskih i algebarskih transformacija. Na kraju je prikazan Masayoshijev problem iz 1821. godine koji je djelomično riješen i algebarski protumačen tek nedavno.
Abstract (english)
Japanese tradition of putting mathematical problems on wooden tiles called sangaku, exhibited in shrines and temples, developed especially in the period from the 17th to the 19th century. From these sources many interesting and sometimes very difficult problems emerged, mostly geometrical, mostly geometrical, and also characterized by their specific style. This paper presents a contemporary treatment of some results and problems that were published in Japan in the nineteenth century, dealing with some particular arrangements of ellipses and other conics and geometric figures. The proofs of certain theorems (Therao) and derivation of some formulas (Shiraishi) are shown to be related and then given in a more concise and precise form, using linear algebra and analytic geometry, as well as some suitable geometric and algebraic transformations. Finally, Masayoshi’s problem from 1821. is presented, which has only recently been partly solved and given a complete algebraic interpretation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:207272
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 on2018-02-02 13:58:12