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Elementarna geometrija štirikotnika
ID Kuralt, Diana (Author), ID Lavrič, Boris (Mentor) More about this mentor... This link opens in a new window

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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.

Language:Slovenian
Keywords:Varignonov paralelogram, težišče, višinska točka, središče očrtane krožnice, središče krožnice devetih točk, Eulerjeva premica, središče včrtane krožnice, Gauss-Newtonova premica, Ponceletova točka, anticenter, Simsonova premica, podobnost
Work type:Master's thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
PID:20.500.12556/RUL-108589 This link opens in a new window
COBISS.SI-ID:18665561 This link opens in a new window
Publication date in RUL:08.07.2019
Views:963
Downloads:235
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Secondary language

Language:English
Title:Elementary geometry of quadrilateral
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.

Keywords:Varignon parallelogram, centroid, orthocenter, circumcenter, nine-point center, Euler line, incenter, Gauss-Newton line, Poncelet point, anticenter, Simson line, similarity

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