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undergraduate thesis
Kvadratne forme i krivulje drugog reda
2019. urn:nbn:hr:126:591918
Pravdić, Tea
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

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Pravdić, T. (2019). Kvadratne forme i krivulje drugog reda (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:591918

Pravdić, Tea. "Kvadratne forme i krivulje drugog reda." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:591918

Pravdić, Tea. "Kvadratne forme i krivulje drugog reda." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:591918

Pravdić, T. (2019). 'Kvadratne forme i krivulje drugog reda', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 11 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:591918

Pravdić T. Kvadratne forme i krivulje drugog reda [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 December 11] Available at: https://urn.nsk.hr/urn:nbn:hr:126:591918

T. Pravdić, "Kvadratne forme i krivulje drugog reda", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:591918

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Metadata
TitleKvadratne forme i krivulje drugog reda
Title (english)Quadratic Forms and Second - Order Curves
AuthorTea Pravdić
MentorSuzana Miodragović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2019-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Kvadratna forma je homogeni polinom drugog stupnja od n varijabli. Kvadratne forme spominju se u raznim granama matematike (teorija brojeva, linearna algebra, diferencijalna geometrija, diferencijalna topologija, ...). U prvom poglavlju ćemo definirati definitnost kvadratne forme. Zatim, prelazimo na skupove točaka ravnine, kao što su kružnica, elipsa, hiperbola i parabola koje imaju niz zajedničkih svojstava, pa ih jednim imenom zovemo krivulje drugog reda. Jedno od zajedničkih svojstava navedenih krivulja je da se svaka od njih može zapisati kao skup svih nultočki polinoma drugog stupnja. Veza izmedu kvadratne forme i krivulja drugog reda omogućuje nam određivanje o kojoj je krivulji riječ i onda kada nam je ona zadana općom jednadžbom, tj. kada nemamo zadanu jednadžbu krivulje sa središtem u ishodištu koordinatnog sustava. Najvažniji dio završnog rada, veza između kvadratne forme i krivulja drugog reda, poopćen je primjerima u svrhu boljeg razumijevanja ove teme.
Abstract (english)
Quadratic form is a homogeneous second degree polynomial of n variables. The quadratic form is used in various branches of mathematics (number theory, linear algebra, differential geometry, differential topology,...). In the first chapter we will define the definiteness of the quadratic form. Next, we move to sets of points of the plane, such as a circle, an ellipse, a hyperbola, and a parabola that have a number of common features, and we call them second order curves by one name. One of the common features of the curves mentioned is that each of them can be written as a set of all null points of second order polynomial. The connection between the quadratic form and the secondorder curves allows us to determine what curve it is and when it is given to us by the general equation, that is, when we do not have a given curve equation centered at the origin of the coordinate system. The most important part of the this paper, the link between the quadratic form and the second-order curves, is generalized with examples for the purpose of a better understanding of this topic
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:591918
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 on2019-10-14 11:06:02