Tetivni štirikotniki

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2013
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[V. Brezar]
UDK:	51(043.2)
COBISS:	9563977
Št. ogledov:	800
Št. prenosov:	101
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Cyclic quadrilaterals
Sekundarni povzetek:	A quadrilateral that can be inscribed in a circle is a cyclic quadrilateral. While all triangles are cyclic, this cannot be said of every quadrilateral. A rectangle and an isosceles trapezoid are cyclic quadrilaterals whereas a rhombus generally is not. In the beginning of the thesis theorems which help distinguish cyclic from non-cyclic quadrilaterals were presented and proved. In the second part of the thesis some general properties of cyclic quadrilaterals were introduced. Firstly, equations for the length of the diagonals, the circumradius R and the area of a cyclic quadrilateral were derived. Furthermore, different manners of calculating the interior angles of a cyclic quadrilateral were studied. A formula to calculate the angle between the diagonals of a cyclic quadrilateral was also derived. Finally, three problems were solved to specify which quadrilaterals can under certain conditions reach their maximum area.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Fak. za matematiko in fiziko, Matematika in fizika
Strani:	VI, 100 str.
Vrsta dela (ePrints):	thesis
Naslov (ePrints):	Cyclic quadrilaterals
Ključne besede (ePrints):	tetivni štirikotnik
Ključne besede (ePrints, sekundarni jezik):	cyclic quadrilateral
Povzetek (ePrints):	Štirikotniku, kateremu je mogoče očrtati krožnico, pravimo tetivni štirikotnik. Medtem ko lahko vsakemu trikotniku očrtamo krožnico, za štirikotnike v splošnem to ne drži. Pravokotnik in enakokraki trapez sta tetivna štirikotnika, romb v splošnem pa ne. Pri prepoznavanju tetivnih štirikotnikov nam pomagajo izreki, ki smo jih podali in dokazali v prvem delu diplomskega dela. V drugem delu smo opredelili nekaj splošnih lastnosti tetivnih štirikotnikov. Zapisali smo, kako lahko izračunamo ploščino tetivnega štirikotnika in podali enačbe za izračun dolžine diagonal ter polmera R tetivnemu štirikotniku očrtane krožnice. Preučili smo tudi, kako lahko izračunamo notranje kote tetivnega štirikotnika in izpeljali enačbo za izračun kota med diagonalama tetivnega štirikotnika. Na koncu smo rešili 3 probleme, pri katerih smo se vprašali, kateri štirikotniki izmed neskončno mnogih pri danih pogojih dosežejo maksimalno ploščino.
Povzetek (ePrints, sekundarni jezik):	A quadrilateral that can be inscribed in a circle is a cyclic quadrilateral. While all triangles are cyclic, this cannot be said of every quadrilateral. A rectangle and an isosceles trapezoid are cyclic quadrilaterals whereas a rhombus generally is not. In the beginning of the thesis theorems which help distinguish cyclic from non-cyclic quadrilaterals were presented and proved. In the second part of the thesis some general properties of cyclic quadrilaterals were introduced. Firstly, equations for the length of the diagonals, the circumradius R and the area of a cyclic quadrilateral were derived. Furthermore, different manners of calculating the interior angles of a cyclic quadrilateral were studied. A formula to calculate the angle between the diagonals of a cyclic quadrilateral was also derived. Finally, three problems were solved to specify which quadrilaterals can under certain conditions reach their maximum area.
Ključne besede (ePrints, sekundarni jezik):	cyclic quadrilateral
ID:	8311227