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master's thesis
Kakeyin problem okretanja igle
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:092923
Knežević, Katarina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Knežević, K. (2024). Kakeyin problem okretanja igle (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:092923

Knežević, Katarina. "Kakeyin problem okretanja igle." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:092923

Knežević, Katarina. "Kakeyin problem okretanja igle." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:092923

Knežević, K. (2024). 'Kakeyin problem okretanja igle', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:092923

Knežević K. Kakeyin problem okretanja igle [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:092923

K. Knežević, "Kakeyin problem okretanja igle", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:092923

Metadata
TitleKakeyin problem okretanja igle
Title (english)Kakeya's needle turning problem
AuthorKatarina Knežević
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberIvana Šain Glibić (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-05-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj diplomski rad bavi se Kakeyinim problemom okretanja igle. Rad počinje opisom povijesnog razvoja problema. Navedeni su i sa slikama potkrijepljeni primjeri Kakeya skupova, tj. likova unutar kojih se jedinična igla neprekidno može zaokrenuti za puni kut. Slijedi konstrukcija Besicovitchevog skupa na dva načina pomoću trokuta te dokaz da površina takvog skupa može biti proizvoljno mala. Zatim se konstruira Kakeya skup, dokazuje se da površina takvog skupa može biti proizvoljno mala i pozitivna te se komentira može li skup u kojem se za puni kut može zaokrenuti igla imati površinu nula. Na kraju rada pomoću slika se prikazuje zakretanje igle za 60\(^\circ\).
Abstract (english)
This thesis deals with Kakeya’s needle problem. The paper begins by describing the historical development of the problem. Examples of Kakeya sets, i.e. figures in which a single needle can be continuously rotated through a full angle, are given and illustrated with pictures. Next, the construction of the Besicovitch set in two ways using triangles and the proof that the area of such a set can be arbitrary small is given. Then the Kakeya set is constructed, it is proved that the area of such a set can be arbitrarily small and positive and it is commented on whether a region in which the needle can be rotated for a full angle can have zero area. At the end of the thesis it is illustrated how the needle rotates by 60◦.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:092923
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-05-21 12:28:32