Astroida

Abstract

Keywords

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Fidel]
UDC:	51(043.2)
COBISS:	9700937
Views:	1084
Downloads:	203
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Astroid
Secondary abstract:	The aim of the present diploma thesis is to present the astroid, a plane curve with the shape of a 4-pointed star. It is defined by a point on the circle that rolls in the inside of another circle, without slipping. A curve formed in this way is called a hypocycloid. Different formations of an astroid are also being discussed. The astroid can be formed as the envelope of line segments, as the envelope of specific family of ellipses or as the catacaustic of Steiner curve. The purpose of the diploma thesis is to examine the astroid and its properties. Pedal curves of astroid are also presented. The conclusion offers possibilities of discussing the astroid in primary school with the help of experiential learning or the use of GeoGebra, the program of dynamic geometry.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in tehnika
Pages:	IX, 76 f.
Type (ePrints):	thesis
Title (ePrints):	Astroid
Keywords (ePrints):	krivulja
Keywords (ePrints, secondary language):	curve
Abstract (ePrints):	V diplomskem delu je predstavljena astroida, ravninska krivulja, ki ima obliko zvezde s štirimi kraki. Opiše jo točka na krožnici, ki se brez drsenja kotali po notranjosti neke druge krožnice. Zato pravimo, da je astroida predstavnica posebne družine krivulj, ki jih imenujemo hipocikloide. Obravnavani so še drugi načini nastanka te krivulje. Astroida nastane bodisi kot ogrinjača družine premic, ogrinjača posebne družine elips ali kot katakavstika Steinerjeve krivulje. Cilj diplomskega dela je čim bolj izčrpna obravnava astroide, zato so v nadaljevanju obravnavane njene lastnosti. Omenjene so nožiščne krivulje astroide. V zaključku so predstavljene možnosti obravnave astroide v osnovni šoli, ob izkustvenem učenju ali z uporabo programa dinamične geometrije GeoGebra.
Abstract (ePrints, secondary language):	The aim of the present diploma thesis is to present the astroid, a plane curve with the shape of a 4-pointed star. It is defined by a point on the circle that rolls in the inside of another circle, without slipping. A curve formed in this way is called a hypocycloid. Different formations of an astroid are also being discussed. The astroid can be formed as the envelope of line segments, as the envelope of specific family of ellipses or as the catacaustic of Steiner curve. The purpose of the diploma thesis is to examine the astroid and its properties. Pedal curves of astroid are also presented. The conclusion offers possibilities of discussing the astroid in primary school with the help of experiential learning or the use of GeoGebra, the program of dynamic geometry.
Keywords (ePrints, secondary language):	curve
ID:	8311600