Neki doprinosi Leonharda Eulera u matematici

master's thesis

• Title (english): Some contributions of Leonhard Euler in mathematics
• Author: Mario Orsag
• Mentor: Igor Ciganović (mentor)
• Committee member: Igor Ciganović (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu opisan je život i znanstveni doprinos Leonharda Eulera. U prvome poglavlju bavimo se Eulerovim doprinosima u teoriji grafova te prikazujemo zbog čega se Eulera naziva ocem topologije. Između ostalog, spominjemo Eulerove grafove, njihovu primjenu te Eulerovu formulu za poliedre. U drugome poglavlju ovog rada, opisujemo Eulerov doprinos teoriji brojeva. Uz nadaleko poznatu Eulerove funkciju te Eulerov teorem, bavimo se i kvadratnim zakonom reciprociteta te Eulerovim otkrićima vezanim uz savršene i prijateljske brojeve. U trećem poglavlju prikazujemo Eulerove rezultate u matematičkoj analizi od kojih se najviše ističu Eulerova zeta funkcija i njen produkt, Eulerov identitet te razvoj funkcija sinus i kosinus. U posljednjem poglavlju bavimo se Eulerovim doprinosom u geometriji pri čemu spominjemu Eulerov pravac, Eulerov teorem i Eulerovu kružnicu

Abstract (english)

This master’s thesis describes the life and scientific contribution of Leonhard Euler. The first chapter describes his contribution in graph theory and shows why Euler is called the father of topology. Among other things, Euler’s graphs are mentioned as is their application. Euler’s formula for polyhedra is also discussed. In the second chapter of this work, Euler’s contribution to number theory is described. In addition to widely known Euler function and Euler’s theorem, the law of quadratic reciprocity and Euler’s discoveries related to perfect and friendly numbers is mentioned. In the third chapter Euler’s result in mathematical analysis is presented, of which I emphasize Euler’s zeta function and its product, Euler’s identity and the development of the sine and cosine function. The last chapter of this paper deals with Euler’s contribution in geometry, where Euler’s line, Euler’s theorem and Euler’s circle are mentioned.

• Keywords: teorija grafova; topology; Eulerova formulu za poliedre; Eulerov pravac; Eulerov teorem i Eulerovu kružnic
• Keywords (english): graph theory; topology; Euler’s formula for polyhedra; Euler’s line; Euler’s theorem; Euler’s circle
• Language: croatian
• URN:NBN: urn:nbn:hr:217:592773
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-02 13:52:55