Astroida

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2013
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[M. Fidel]
UDK:	51(043.2)
COBISS:	9700937
Št. ogledov:	1084
Št. prenosov:	203
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Astroid
Sekundarni povzetek:	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.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Matematika in tehnika
Strani:	IX, 76 f.
Vrsta dela (ePrints):	thesis
Naslov (ePrints):	Astroid
Ključne besede (ePrints):	krivulja
Ključne besede (ePrints, sekundarni jezik):	curve
Povzetek (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.
Povzetek (ePrints, sekundarni jezik):	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.
Ključne besede (ePrints, sekundarni jezik):	curve
ID:	8311600