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undergraduate thesis
Helikodalne plohe
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. urn:nbn:hr:126:574932
Šoštarić, Matija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Šoštarić, M. (2022). Helikodalne plohe (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:574932

Šoštarić, Matija. "Helikodalne plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:574932

Šoštarić, Matija. "Helikodalne plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:574932

Šoštarić, M. (2022). 'Helikodalne plohe', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 28 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:574932

Šoštarić M. Helikodalne plohe [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 November 28] Available at: https://urn.nsk.hr/urn:nbn:hr:126:574932

M. Šoštarić, "Helikodalne plohe", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:574932

Metadata
TitleHelikodalne plohe
Title (english)Generalized Helicoids
AuthorMatija Šoštarić
MentorLjiljana Primorac Gajčić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovome radu promatrat ćemo plohe koje nastaju helikoidalnim gibanjem tzv. helikoidalne plohe. Helikoidalno gibanje sastoji se od istovremene translacije u smjeru nekog pravca i rotacije oko istog pravca. Osim u diferencijalnoj geometriji, helikoidalne plohe nalazimo posvuda oko nas. Medicina, mehanika i brodogradnja samo su neka zanimanja koja se svakodnevno susreću sa helikoidalnim plohama te helikoidalnim gibanjem. Formule koje ćemo navesti vrlo važnu ulogu imaju u svakodnevnim inženjerskim projektima. Iskazat ćemo bitne definicije i teoreme helikoidalnih ploha te navesti određene pomoćne tvrdnje. Nadalje, navest ćemo parametrizaciju helikoidalne plohe generirane ravninskom krivuljom, pogledat ćemo primjere helikoidalnih ploha te se posebno osvrnuti na plosnate helikoidalne plohe. Slike koje nemaju naveden izvor izrađene su u programu Mathematica.
Abstract (english)
In this work we will observe surfaces which are the result of a screw motion, also called generalized helicoids. Screw motion consists of simultaneous translation in the direction of a certain line and rotation around the same line. Generalized helicoids can be found everywhere around us. Medicine, mechanics and shipbuilding are just some of the fields that are on a daily basis encountered by generalized helicoids and screw motion. The mentioned formulas play a very important role in everyday engineering projects. Some important definitions and theorems of generalized helicoids will be presented, as well as some auxiliary statements.Furthermore, the parameterization of generalized helicoid genererated by a curve will be specified, and some examples of generalized helicoids will be given with special emphasis on flat generalized helicoids. Images that do not have a source listed were created in Mathematica.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:574932
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 on2022-10-07 12:13:06