Islamski matematičari mongolskoga doba

master's thesis

• Author: Renata Antolek
• Mentor: Franka Miriam Bruckler (mentor)
• Committee member: Franka Miriam Bruckler (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskom radu Islamski matematičari mongolskoga doba cilj je upoznati se s doprinosima islamskih matematičara u razoblju 13.-15. stoljeća. Na početku rada prisjećamo se povijesti trigonometrije i mongolskog carstva te matematike srednjovjekovnog muslimanskog svijeta kako bismo lakše u nastavku pratili daljnji razvoj. Islamski su matematičari mongolskog doba pisali radove u mnogim područjima, kao što su matematika, etika, filozofija, astronomija... U poglavlju sa životopisima su ukratko opisana njihova glavna postignuća. Važni matematički doprinosi posebno su istaknuti u trećem i četvrtom poglavlju. Najviše radova tog doba bilo je o trigonometriji, a posebno su važni radovi al-Kāšīja i aṭ-Ṭūsīja. Al-Kāšījeve trigonometrijske tablice i metoda iteracije veliki su doprinos matematici, kao i aṭ-Ṭūsījev dokaz poučka o sinusu. Njihovi su radovi također bitni i u algebri, posebno radovi o binomnim koeficijentima. U algebri bitan doprinos dao je i al-Fārisī koji je djelom dokazao osnovni teorem aritmetike. U zadnjem poglavlju dan je zaključak diplomskog rada u kojem je izneseno mišljenje autora.

Abstract (english)

The aim of the master’s thesis Islamic Mathematicians during Mongol Rule is to get a better insight into contributions of Islamic Mathematicians from the 13th to the 15th centuries. This text begins with short reviews of the history of trigonometry and the Mongol Empire. The introductory chapter also reviews the history of mathematics in the medieval Islamic world, in order to be able to follow further developments more easily. Islamic mathematicians during the Mongol time wrote papers about various areas such as mathematics, ethics, physics, philosophy, astronomy… Their achievements are briefly described in the chapter which contains their biographies. Important contributions in mathematics are highlighted in the third and fourth chapters. During this period the majority of papers dealt with trigonometry. Papers written by al-Kāšī and aṭ-Ṭūsī were especially important. Al-Kāšī’s trigonometric tables and iterative method, as well as aṭ-Ṭūsī’s proof of the law of sines, are great contributions to mathematics. Their work is also important for algebra, especially their papers on binomial coefficient. Al-Fārisī, who also made an important contribution to algebra, partly proved the fundamental theorem of arithmetic. The last chapter contains a conclusion in which the author gives her opinion.

• Keywords: Islamski matematičari; mongolsko doba; al-Kaši; al-Kāšī; at-Tusi; aṭ-Ṭūsī; trigonometrijske tablice; metoda iteracije; poučak o sinusu; binomni koeficijenti; al-Farisi; al-Fārisī; osnovni teorem aritmetike
• Keywords (english): Islamic mathematicians; Mongol Rule; al-Kaši; al-Kāšī; at-Tusi; aṭ-Ṭūsī; trigonometric tables; iterative method; law of sines; binomial coefficient; al-Farisi; al-Fārisī; fundamental theorem of arithmetic
• Language: croatian
• URN:NBN: urn:nbn:hr:217:028812
• 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: 2017-10-17 09:16:44