Katakavstike

Abstract

Keywords

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[N. Andrejčič]
UDC:	514.7(043.2)
COBISS:	9465417
Views:	568
Downloads:	177
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Catacaustics
Secondary abstract:	The thesis presents catacaustics, plane curves that are produced by the reflection of rays of light in a curved mirror. We have different catacaustics for differently shaped curved mirrors. They can be described mathematically as the envelope of all rays that reflect from a given curve. The mathematical derivation of equations is given. The equations of catacaustics for different plane curves (circle, parabola, exponential curve, cycloid) are written in parametric form. The graphical representation is made with mathematical program GeoGebra.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in tehnika
Pages:	X, 69 str.
Type (ePrints):	thesis
Title (ePrints):	Catacaustics
Keywords (ePrints):	odboj svetlobe
Keywords (ePrints, secondary language):	reflection
Abstract (ePrints):	V diplomskem delu so predstavljene katakavstike, ravninske krivulje, ki nastanejo z odbojem snopa svetlobnih žarkov od ukrivljenega zrcala. Pri različno oblikovanih ukrivljenih zrcalih nastanejo različne katakavstike. Katakavstike so obravnavane matematično, kot ogrinjače družine premic odbitih žarkov. Izračunane so parametrične enačbe za nekaj primerov katakavstik, ki nastanejo pri odboju od znanih krivulj (krožnica, parabola, naravna eksponentna krivulja, cikloida). Le-te so tudi narisane v programu GeoGebra.
Abstract (ePrints, secondary language):	The thesis presents catacaustics, plane curves that are produced by the reflection of rays of light in a curved mirror. We have different catacaustics for differently shaped curved mirrors. They can be described mathematically as the envelope of all rays that reflect from a given curve. The mathematical derivation of equations is given. The equations of catacaustics for different plane curves (circle, parabola, exponential curve, cycloid) are written in parametric form. The graphical representation is made with mathematical program GeoGebra.
Keywords (ePrints, secondary language):	reflection
ID:	8310927