diplomsko delo
Tadeja Sever (Author), Bojan Hvala (Mentor)

Abstract

Predmet obravnave diplomskega dela je diagonalni trikotnik OPR poljubnega konveksnega štirikotnika ABCD. Ugotovili bomo, kakšna je ploščina trikotnika, in rešili uvodni problem. V nadaljevanju se bomo osredotočili na diagonalni trikotnik tetivnega štirikotnika. Predstavili bomo nekaj značilnosti tetivnih štirikotnikov, s katerimi bomo izpeljali formulo za ploščino diagonalnega trikotnika tetivnega štirikotnika v odvisnosti od njegovih stranic. Na koncu bomo predstavili še zanimiv odnos med tetivnemu štirikotniku očrtano krožnico in diagonalnim trikotnikom tega štirikotnika. Dokazali bomo, da je glede na to krožnico omenjeni trikotnik sebipolaren.

Keywords

diplomska dela;diagonalni trokotniki;konveksni štirikotniki;ploščina;tetivni štirikotniki;Miquelova točka;inverzija;polarnost;sebipolarni trikotniki;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [T. Sever]
UDC: 514.112.3(043.2)
COBISS: 22188808 Link will open in a new window
Views: 1006
Downloads: 107
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Other data

Secondary language: English
Secondary title: Diagonal triangle of a convex quadrilateral
Secondary abstract: The subject of graduation thesis is a diagonal triangle OPR of the general convex quadrilateral ABCD. We will find the area of the triangle and we will solve an introductory problem. In the continuation of the graduation thesis we will focus on the diagonal triangle of a cyclic quadrilateral. We will present some features of cyclic quadrilaterals in order to improve the formula for the area of the diagonal triangle of a cyclic quadrilateral. Finally, we will present an interesting relationship between a circumcircle of a cyclic quadrilateral and diagonal triangle of the same quadrilateral. According to the circumcircle, we will prove that the triangle in question is self-conjugate.
Secondary keywords: theses;diagonal triangles;convex quadrilateral;area;cyclic quadrilateral;Miquel point;inversion;polarity;self-conjugate triangles;
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.
ID: 9134791