Tangentni štirikotniki

diplomsko delo

Nina Krmelj (Author), Bojan Hvala (Mentor)

Abstract

Tangentni štirikotnik je konveksni štirikotnik, ki mu lahko včrtamo krog. Štirikotnik je tangenten natanko takrat, ko se simetrale njegovih notranjih kotov sekajo v eni točki. Prav tako je štirikotnik tangenten natanko takrat, ko sta vsoti dolžin nasprotnih stranic enaki. Ob omenjenih dveh najbolj znanih karakterizacij je v diplomskem delu predstavljenih še nadaljnjih pet karakterizacij tangentnih štirikotnikov. Med njimi je tudi Chaojeva karakterizacija tangentnega štirikotnika s polmeri včrtanih krogov štirih trikotnikov. Na koncu so dodane formule za izračun polmera tangentnemu štirikotniku včrtanega kroga, med katerimi je tudi formula, ki je nastala kot del rešitve naloge na nekem matematičnem tekmovanju na Kitajskem.

Keywords

matematika;tangentni štirikotniki;krožnica;radij;trikotniki;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Krmelj]
UDC:	51(043.2)
COBISS:	18407432
Views:	3987
Downloads:	282
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	TANGENTIAL QUADRILATERALS
Secondary abstract:	A tangential quadrilateral is a convex quadrilateral in which a circle can be inscribed. A quadrilateral is tangential if and only if the four angle bisectors meet at one point. Furthermore a quadrilateral is tangential if and only if its two pairs of opposite sides have equal sums. Apart from these two characterizations of tangential quadrilaterals in this diploma work we present other five characterizations of tangential quadrilaterals. One of them is Chao's characterization with the radii of the circles inscribed in the four triangles. A list of formulas is added at the end of this work necessary for the calculation of a radius of the inscribed circle of the tangential quadrilateral; among them is also a formula which was part of the solution of a contest problem in China.
Secondary keywords:	tangential qudrilateral;inscribed circle;radius of an inscribed circle;triangle excircles.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	51 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19294