magistrsko delo
Diana Kuralt (Author), Boris Lavrič (Mentor)

Abstract

Magistrsko delo razišče lastnosti konveksnega in konkavnega štirikotnika. Najprej predstavi lik, ki ga tvorijo razpolovišča stranic štirikotnika. Nato obravnava pomembne točke v štirikotniku, kot so težišče, višinska točka, središče očrtane krožnice in središče krožnice devetih točk ter pokaže, da omenjene točke ležijo na skupni premici. V nadaljevanju se delo osredotoči na trikotnike, ki imajo za oglišča tri izmed oglišč štirikotnika. Definira točko, ki leži na krožnicah devetih točk teh trikotnikov in to točko v drugem delu obravnava še za primer tetivnih štirikotnikov. Magistrska naloga opisuje tudi središči včrtanih krožnic v konveksnem štirikotniku in poda obrazec za ploščino konveksnega štirikotnika. Nazadnje omenja podobnosti štirikotnikov z dodatnim premislekom za tetivne štirikotnike.

Keywords

Varignonov paralelogram;težišče;višinska točka;središče očrtane krožnice;središče krožnice devetih točk;Eulerjeva premica;središče včrtane krožnice;Gauss-Newtonova premica;Ponelotova točka;anticenter;Simsonova premica;podobnost;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [D. Kuralt]
UDC: 514
COBISS: 18665561 Link will open in a new window
Views: 1062
Downloads: 238
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Other data

Secondary language: English
Secondary title: Elementary geometry of quadrilateral
Secondary abstract: The Master thesis examines properties of convex and concave quadrilaterals. Firstly, it studies a shape that is formed by the midpoints of a quadrilateral. Then it deals with significant points in a quadrilateral such as centroid, orthocenter, circumcenter and nine-point center, and proves that aforementioned points lie on the same line. Furtheron, the thesis focuses on the triangles, whose vertices are determined by three out of the four vertices of a quadrilateral. It defines the point that lies on nine-point circles of these triangles. In the second part, this point is independently discussed for the case of cyclic quadrilaterals. In addition, the master thesis describes incenters in a convex quadrilateral, and states a formulation for the area of a convex quadrilateral. At the end, it addresses the similarities of quadrilaterals with additional thought on cyclic quadrilaterals.
Secondary keywords: Varignon parallelogram;centroid;orthocenter;circumcenter;nine-point center;Euler line incenter;incenter;Gauss-Newton line;Poncelet point;anticenter;Simson line;similarity;
Type (COBISS): Master's thesis/paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages: IX, 59 str.
ID: 11187006