Matematika kaleidoskopa

Sorić, Linda (2015) Matematika kaleidoskopa. Diploma thesis, Faculty of Science > Department of Mathematics.

[img] PDF
Restricted to Registered users only
Language: Croatian

Download (11MB) | Request a copy

Abstract

Kaleidoscopes are optical instruments for creating and observing visually attractive patterns. Two mathematical concepts that are closely related to kaleidoscopes are symmetries and groups, so they determine two main chapters of this paper. Depending on the number of mirrors inside the kaleidoscope, and the dimension of the space we observe it in, kaleidoscope can form two-dimensional, three-dimensional or abstract multidimensional patterns. This paper is focused on two-dimensional and three-dimensional patterns and their symmetries. Our goal is the determination of the symmetries of a pattern based on type of kaleidoscope that formed it, and also the determination of the type of kaleidoscope based on symmetries of the resulting pattern. Symmetries of patterns created by kaleidoscopes, together with the operation of composition, form a group. Next, we give an overview of known symmetry groups related to two-dimensional and three-dimensional patterns: rosette groups, wallpaper groups, three dimensional point groups and space groups. Two-dimensional kaleidoscopes with two mirrors generate rosette groups. Two-dimensional kaleidoscopes with three and four mirrors generate certain wallpaper groups. Three-dimensional kaleidoscopes with three mirrors generate certain three-dimensional point groups. ”Closed box” kaleidoscopes generate certain space groups.

Item Type: Thesis (Diploma thesis)
Supervisor: Brückler, Franka Miriam
Date: 2015
Number of Pages: 54
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 03 Sep 2015 13:00
Last Modified: 03 Sep 2015 13:00
URI: http://digre.pmf.unizg.hr/id/eprint/4222

Actions (login required)

View Item View Item