Trokutasti brojevi

master's thesis

• Title (english): Triangular numbers
• Author: Matea Pavlović
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-12-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Trokutasti brojevi specijalna su klasa figurativnih brojeva koji se dobivaju slaganjem točkica u jednakostraničan trokut. Trokutasti broj \(T_n\) jednak je zbroju prvih \(n \) prirodnih brojeva, odnosno n(n+1)/2. Možmo ih vizualizirati, pronaći u svijetu koji nas okružje te algebarskom manipulacijom iskazati niz različtih svojstava i identiteta koje zadovoljavaju. U radu je, koristeći navedeno, prikazana njihova veza s Pellovom i Pitagorinom jednadžbom te mnogim poznatim brojevima poput Fermatovih, Fibonaccijevih, Mersenneovih i Pellovih brojeva.

Abstract (english)

Triangular numbers are a special class of figurate numbers that can be represented by dots arranged in an equilateral triangle. A triangular number \(T_n \) is the sum of first \(n \) natural numbers, i.e. n(n+1)/2. We can visualize them, find triangular arrangements of objects in the real world and establish some interesting properties and identities algebraically. Using the above, their connections with the Pell and Pythagorean equations and also with many known numbers such as Fermat, Fibonacci, Mersenne and Pell numbers are represented in this thesis.

• Keywords: figurativni brojevi; Pellova jednadžba; Pitagorina jednadžba; Fermatovi brojevi; Fibonaccijevi brojevi; Mersenneovi brojevi; Pellovi brojevi
• Keywords (english): figurative numbers; Pell's equation; Pythagorean equation; Fermat numbers; Fibonacci numbers; Mersenne numbers; Pell numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:373388
• 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: 2021-12-15 12:59:23