Neki stari japanski teoremi o elipsama

master's thesis

• Author: Marko Marinov
• Mentor: Juraj Šiftar (mentor)
• Committee member: Juraj Šiftar (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-07-17, 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: sangaku; Teraov teorem; Shiraishijeva formula; Masayoshijev problem; linearna algebra; analitička geometrija; geometrijske transformacije; algebarske transformacije
• Keywords (english): sangaku; Therao's theorem; Shiraishi's formula; Masayoshi's problem; linear algebra; analytic geomtry; geometric transformations; algebraic transformations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:207272
• 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: 2018-02-02 13:58:12