Pascalov trokut

master's thesis

• Title (english): Pascal's triangle
• Author: Katarina Marijanović
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-04-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavali smo konstrukciju Pascalovog trokuta i njegova svojstva. U prvom smo poglavlju dali povijesni prikaz nastanka i tijeka proučavanja Pascalovog trokuta. U drugom poglavlju definirali smo Pascalovu operaciju pomoću koje smo prikazali dvije najpoznatije primjene Pascalovog trokuta: binomne koeficijente i kombinacije. Nakon toga, u trećem smo poglavlju opisali i dokazali razna zanimljiva svojstva Pascalovog trokuta. Svojstva smo podijelili u nekoliko skupina. Prva skupina su osnovna, lako uočljiva, svojstva Pascalovog trokuta. Drugoj skupini pripadaju zanimljivi brojevi i poznati iracionalni brojevi koje nalazimo proučavajući elemente Pascalovog trokuta. Treća skupina predstavlja svojstva povezana s geometrijom. Naposljetku, zadnjoj skupini pripadaju netrivijalna svojstva Pascalovog trokuta. U zadnjem smo poglavlju pokazali kako se Pascalova operacija može koristiti pri rješavanju problemskih zadataka na primjeru zadatka s matematičke olimpijade.

Abstract (english)

In this thesis, we studied the construction of the Pascal triangle and its properties. In the first chapter, we give a historical overview of the origin and course of the study of the Pascal triangle. In the second chapter, we defined Pascal’s operation by which we presented the two most famous applications of the Pascal triangle: binomial coefficients and combinations. After that, in the third chapter, we described and proved various interesting properties of the Pascal triangle. We divided the properties into several groups. The first group are the basic, easily noticeable, properties of the Pascal triangle. The second group includes interesting numbers and well-known irrational numbers that we find by studying the elements of Pascal’s triangle. The third group represents properties related to geometry. Finally, the nontrivial properties of the Pascal triangle belong to the latter group. In the last chapter, we showed how Pascal’s operation can be used to solve problem tasks on the example of a task from the Mathematical Olympiad.

• Keywords: Pascalova operacija; geometrija; binomni koeficijenti; matematička olimpijada
• Keywords (english): Pascal’s operation; binomial coefficients; geometry; Mathematical Olympiad
• Language: croatian
• URN:NBN: urn:nbn:hr:217:252138
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-06-09 11:06:08