Geometrija prirode

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.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