Tetivni štirikotniki

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Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[V. Brezar]
UDC:	51(043.2)
COBISS:	9563977
Views:	800
Downloads:	101
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Cyclic quadrilaterals
Secondary abstract:	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.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Fak. za matematiko in fiziko, Matematika in fizika
Pages:	VI, 100 str.
Type (ePrints):	thesis
Title (ePrints):	Cyclic quadrilaterals
Keywords (ePrints):	tetivni štirikotnik
Keywords (ePrints, secondary language):	cyclic quadrilateral
Abstract (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.
Abstract (ePrints, secondary language):	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.
Keywords (ePrints, secondary language):	cyclic quadrilateral
ID:	8311227