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Traktrisa : diplomsko delo
ID Apšner, Nadja (Author), ID Razpet, Marko (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/3545/ This link opens in a new window

Abstract
V diplomskem delu je predstavljena transcendentna ravninska krivulja traktrisa in njej sorodne krivulje. Na ravnini traktriso opisuje točkasta masa, ki je privezana na neraztegljivi niti konstantne dolžine, katere prosti konec vlečemo po premici v tej ravnini. Običajno je ta premica abscisna os. Namen diplomskega dela je čim bolj temeljita obravnava traktrise. V ta namen so opisane lastnosti le-te ter v povezavi z njo narejeni izračuni ploščine, ločne dolžine, ter površine in prostornine telesa, ki ga dobimo z vrtežem traktrise okoli njene asimptote. Ploskev imenujemo psevdosfera, ki ima konstantno negativno Gaussovo ukrivljenost. Opisan je nastanek traktrise s preprostimi mehanskimi orodji in nastanek modela psevdosfere. Na koncu so predstavljene še traktrisi sorodne krivulje in njihov nastanek.

Language:Slovenian
Keywords:koordinatni sistem, ravninske krivulje, psevdosfera
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Publisher:[N. Apšner]
Year:2016
Number of pages:XII, [63] str.
PID:20.500.12556/RUL-84100 This link opens in a new window
UDC:514.752.2(043.2)
COBISS.SI-ID:11069257 This link opens in a new window
Publication date in RUL:24.08.2016
Views:1407
Downloads:147
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Secondary language

Language:English
Title:Tractrix
Abstract:
The diploma thesis presents a transcendent plane curve, called tractrix, and its related curves. On the plane the tractrix is defined by a dotted mass that is attached to the tensile nor constant size, the free end is drawn by the straight line in that plane. This is usually a straight line abscissa. The purpose of this diploma thesis is to thoroughly study the tractrix. For this purpose there are basic descriptions of it and in connection also made calculations of the area, arc lenght, area of the surface and volume, which we get with rotating tractrix around it’s asymptote. The surface is called pseudosphere and it has a constant negative Gaussian curvature. Described is also the emergence of the tractrix with simple mechanical tools and the creation of a model of pseudosphere. In conclusion there are being presented different formations of tractrix and also connections with others curves.

Keywords:plane curve

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