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undergraduate thesis
Plohe konstantne srednje zakrivljenosti
2020. urn:nbn:hr:126:473465
Kokanović, Karlo
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

Cite this document

Kokanović, K. (2020). Plohe konstantne srednje zakrivljenosti (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:473465

Kokanović, Karlo. "Plohe konstantne srednje zakrivljenosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:473465

Kokanović, Karlo. "Plohe konstantne srednje zakrivljenosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:473465

Kokanović, K. (2020). 'Plohe konstantne srednje zakrivljenosti', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:473465

Kokanović K. Plohe konstantne srednje zakrivljenosti [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:126:473465

K. Kokanović, "Plohe konstantne srednje zakrivljenosti", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:473465

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Metadata
TitlePlohe konstantne srednje zakrivljenosti
Title (english)Surfaces of Constant Mean Curvature
AuthorKarlo Kokanović
MentorZdenka Kolar-Begović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovome radu ćemo razmatrati pojam ploha konstantne srednje zakrivljenosti te navesti brojne primjere takvih ploha. Osim u diferencijalnoj geometriji, plohe konstantne srednje zakrivljenosti poznate su i u teoriji optimizacije, budući da predstavljaju rješenja izoperimetrijskog problema. U radu su također navedene osnovne definicije i teoremi lokalne teorije ploha koje ćemo primjenjivati. Nadalje, bavit ćemo se i specijalnim slučajem ploha konstantne srednje zakrivljenosti, tzv. minimalnim plohama i navesti njihovu vezu s određenim pojavama u prirodi. Na kraju ćemo analizirati neke primjere minimalnih ploha za specijalne klase ploha kao što su: rotacijske plohe, translacijske plohe i pravčaste plohe. Za sve primjere ploha koje navodimo u radu prikazat ćemo i njihovu sliku koja je izrađena u programu Mathematica.
Abstract (english)
In this work, we will introduce the concept of a surface of constant mean curvature and present various examples of such surfaces. Beside differential geometry, surfaces of constant mean curvature are well-known in optimization theory since they represent solutions of the isoperimetric problem. In the work we also give basic definitions and theorems which will be applied. Furthermore, we will deal with special class of surfaces of constant mean curvature, the so-called minimal surfaces and show their connection with certain nature phenomena. Finally, we will analyze some examples of minimum surfaces for special classes of surfaces such as: rotational surfaces, translation surfaces, and ruled surfaces. For all the examples of surfaces that we list in the work, we will also show their image created by software Mathematica.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:473465
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-11-05 08:18:12