Neke matematičke konstante i njihovi verižni razlomci

master's thesis

• Author: Maja Dravec
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Vinko Petričević (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Činjenica je da se neki brojevi pojavljuju u matematici i njezinim primjenama češće od ostalih brojeva. Ti brojevi su matematičke konstante. U ovom diplomskom radu bavimo se s četiri najpoznatije konstante: Pitagorinom konstantom \(\sqrt {2} \), zlatnim rezom \(\varphi \), Napierovom konstantom ili Eulerovim brojem \( e\) i Arhimedom konstantom ili Ludolphovim brojem \(\pi \) i prikazujemo ih u obliku verižnih razlomaka. Verižni razlomci koristan su alat za pronalaženje racionalnih aproksimacija iracionalnih brojeva.

Abstract (english)

The fact is that some numbers arise throughout mathematics and its application areas more frequently than the others. These numbers are mathematical constants. In this thesis, we deal with the four most famous constants: Pythagoras’ constant, the golden ratio, Napier’s constant or Euler’ s number and Archimedes’ constant or Ludolph’s number, and give its continued fraction expansions. Continued fractions are a useful tool for finding rational approximations to irrational numbers

• Keywords: matematičke konstante; Pitagorina konstanta; zlatni rez; Napierova konstanta; Eulerov broj; Arhimedova konstanta; Ludolphov broj
• Keywords (english): mathematical constants; Pythagoras’ constant; the golden ratio; Napier’s constant or Euler’ s number; Archimedes’ constant or Ludolph’s number
• Language: croatian
• URN:NBN: urn:nbn:hr:217:562956
• 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: 2020-12-10 12:33:28