Ravninske krivulje

master's thesis

• Author: Renata Škrivanek
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu sam opisala neke od načina tvorba krivulja: – krivulje koje nastaju presjekom dane plohe ravninom; – krivulje koje nastaju kao geometrijsko mjesto točaka koje zadovoljavaju dano svojstvo; – krivulje koje nastaju kao putanja točke koja se giba po nekom određenom zakonu; – krivulje koje nastaju zadavanjem njenih diferencijalnih svojstava; – krivulje koje se zadaju u analitičkom obliku. Opisala sam i svojstva promatranih krivulja. Ta svojstva se očituju u mehanizmima, detaljima strojeva, građevnim konstrukcijama, u optici, slikarstvu, arhitekturi, u crtanju, u geometrijskim konstrukcijama,... Neke krivulje se realiziraju u prirodi. U radu sam krivulje i njihova svojstva proučavala strogo matematički, bez njihove primjene. Promatranim krivuljama sam napisala nešto o njihovoj povijesti. Pri pisanju ovog rada, svojstva krivulja su me često fascinirala i još jače pobudila zanimanje za upoznavanjem krivulja.

Abstract (english)

In this thesis, some of curve formations are described: – curves which occur by intersecting the given surface by the plane; – curves which occur as a geometric locus of points satisfying the given feature; – curves which occur as the path of a point that moves according to a certain definite principle; – curves which occur by setting their differential features; – curves which are set in an analytical form. The observed curve features are described as well. These features manifest in mechanisms, device details, building constructions, optics, painting, architecture, drawing, geometric constructions. Some curves accomplish in nature. Curves and their features are studied in this thesis strictly mathematically without applications. I wrote about the history of the observed curves, as well. While doing this thesis, I was fascinated by curve features so my interest in learning about them aroused greatly.

• Keywords: ravninske krivulje; krivulje koje nastaju presjekom dane plohe ravninom; krivulje koje nastaju kao geometrijsko mjesto točaka koje zadovoljavaju dano svojstvo; krivulje koje nastaju kao putanja točke koja se giba po nekom određenom zakonu; krivulje koje nastaju zadavanjem njenih diferencijalnih svojstava; krivulje koje se zadaju u analitičkom obliku
• Keywords (english): plane curves; curves which occur by intersecting the given surface by the plane; curves which occur as a geometric locus of points satisfying the given feature; curves which occur as the path of a point that moves according to a certain definite principle; curves which occur by setting their differential features; curves which are set in an analytical form
• Language: croatian
• URN:NBN: urn:nbn:hr:217:799281
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-13 12:56:37