Geometrija prirode

master's thesis

• Author: Biljana Stipetić
• Mentor: Franka Miriam Bruckler (mentor)
• Committee member: Franka Miriam Bruckler (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome smo radu opisali pojave različitih geometrijskih objekata u makroskopskoj prirodi. Cilj je bio dati sistematičan prikaz prirodnih geometrijskih oblika uz slike i matematičku argumentaciju njihove pojave. Pri tome je težište stavljeno na pojmove koji se mogu iskoristiti u nastavi matematike kroz osnovnoškolsko i srednjoškolsko obrazovanje. Uz primjere pojave geometrijskih likova i tijela te simetričnih uzoraka, opisani su i Boškovićev matematički model pčelinjeg saća, pojave logaritamskih spirala i zlatnog reza u prirodi, … Rad je podijeljen u tri poglavlja: pripremni dio, geometriju te naprednije geometrijske teme. U pripremnom dijelu opisane su neke matematičke teme koje nisu neposredno geometrijske, ali su neophodne za praćenje glavne teme rada: brojevi, nizovi i potencije. U glavnom dijelu opisane su geometrijske teme koje su vezane za školsko gradivo matematike, dok su u poglavlju s naprednijim temama obrađene pojave pozitivne i negativne zakrivljenosti te fraktala u prirodi.

Abstract (english)

In this thesis we described appearances of geometrical shapes in macroscopic nature. The goal was to give a systematic over view of nature’s geometrical shapes with the help of pictures and the mathematical argumentation of their appearances. The emphasis was on terms that can be used in mathematics teaching in elementary and high school education. Besides examples of appearance of geometrical shapes and symmetry were also described Bošković’s mathematical models of the honeycomb, the appearance of logarithmic spirals ´ and the golden ration in nature, .... The thesis is divided in three chapters: introductory part, geometry and advanced geometrical topics. In the introductory part are mathematical topics described which are not essentially geometrical but are necessary for the understanding of the main part of the thesis: numbers, sequences and exponentiations. In the main part of the paper are geometrical topics described that are connected with material covered in math classes in school. In the chapter about advanced topics, we discuss appearances of positive and negative curvature and the appearance of fractals in nature.

• Keywords: nastava matematike u osnovnoškolskom i srednjoškolskom obrazovanju; Boškovićev matematički model pčelinjeg saća; logaritamska spirala; zlatni rez; pozitivna zakrivljenost; negativna zakrivljenost; fraktali; nastava matematike; osnovna škola; srednja škola
• Keywords (english): mathematics teaching in elementary and high school education; Bošković’s mathematical models of the honeycomb; logarithmic spirals; golden ratio; positive curvature; negative curvature; fractals; teaching mathematics; elementary school; primary school; high school; middle school
• Language: croatian
• URN:NBN: urn:nbn:hr:217:167484
• 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: Access restricted to students and staff of home institution
• Created on: 2019-02-07 12:57:30