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master's thesis
Simetrije periodičkih popločavanja ravnine
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:746688
Kruhoberec, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Cite this document

Kruhoberec, A. (2017). Simetrije periodičkih popločavanja ravnine (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:746688

Kruhoberec, Ana. "Simetrije periodičkih popločavanja ravnine." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:746688

Kruhoberec, Ana. "Simetrije periodičkih popločavanja ravnine." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:746688

Kruhoberec, A. (2017). 'Simetrije periodičkih popločavanja ravnine', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:217:746688

Kruhoberec A. Simetrije periodičkih popločavanja ravnine [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:746688

A. Kruhoberec, "Simetrije periodičkih popločavanja ravnine", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:746688

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Metadata
TitleSimetrije periodičkih popločavanja ravnine
AuthorAna Kruhoberec
MentorFranka Miriam Bruckler (mentor)
Committee memberFranka Miriam Bruckler (predsjednik povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberSonja Štimac (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Simetrije svake ravninske figure čine grupu obzirom na kompoziciju. Ukoliko figura posjeduje translacijsku simetriju, govorimo o periodičnoj figuri, preciznije o frizu ili tapeti, ovisno o tome pojavljuje li se ta translacijska simetrija samo u jednom smjeru ili ne. U ovom je radu opisana klasifikacija frizova i tapeta obzirom na njihove grupe simetrija. Pomoću tzv. Conwayevog magičnog teorema pokazano je da postoji točno 7 grupa frizova i 17 grupa tapeta. Za frizove smo isto pokazali i elementarnijim, geometrijskim pristupom. Primjeri uzoraka frizova i tapeta izrađeni su pomoću aplikacije Kali, koja je zbog jednostavnosti primjerena svim generacijama, te je iz tog razloga primjenjiva i u nastavi matematike vezano uz teme simetrija.
Abstract (english)
Every plane figure’s symmetries form a group with respect to composition. If a figure possesses translational symmetry, one speaks of a periodic pattern, more precisely of a frieze or wallpaper, depending on if translational symmetries occur in only one direction or not. This thesis describes the classification of friezes and wallpapers with respect to their symmetry groups. The fact that there exist exactly 7 frieze groups and 17 wallpaper groups is shown using the so-called Conway magic theorem. The result on friezes is also proved using a more elementary, geometric approach. Examples of frieze and wallpaper patterns have been generated with the Kali application which is, due to its simplicity, suitable for all generations, and as such usable in teaching symmetry topics in the mathematics classroom.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:746688
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsClosed access
Terms of useLicence In copyright icon
RepositoryRepository of the Faculty of Science
Created on2018-02-01 14:03:03

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