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Steinerjevi izreki o kompletnem štirikotniku
ID Čebulj, Aleš (Author), ID Vavpetič, Aleš (Mentor) More about this mentor... This link opens in a new window

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Abstract
Diplomska naloga obravnava geometrijski objekt kompletni štirikotnik ter nekaj njegovih lastnosti. Kompletni štirikotnik je konfiguracija, ki jo predstavljajo štiri premice. Te štiri premice naj bodo nevzporedne ter naj se sekajo dve po dve v šestih točkah. Glavni poudarek diplome je na desetih izrekih o kompletnem štirikotniku, ki jih je prvi formuliral Jakob Steiner leta 1828. Diplomsko delo vseh deset izrekov formulira, predstavi, dokaže ter izpelje tudi nekaj posledic. Poleg Steinerjevih izrekov ter njihovih dokazov pa je v nalogi predstavljenih tudi kar nekaj drugih bolj osnovnih geometrijskih konceptov in rezultatov, kot so na primer pojem inverza, polare, krožnice devetih točk, Menelajev izrek, ki jih potrebujemo pri dokazovanju Steinerjevih izrekov.

Language:Slovenian
Keywords:kompletni štirikotnik, Miquelova točka, direktna podobnost, polara, Simsonova premica
Work type:Bachelor thesis/paper
Typology:2.11 - Undergraduate Thesis
Organization:FRI - Faculty of Computer and Information Science
FMF - Faculty of Mathematics and Physics
Year:2023
PID:20.500.12556/RUL-149984 This link opens in a new window
COBISS.SI-ID:167064323 This link opens in a new window
Publication date in RUL:12.09.2023
Views:477
Downloads:63
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Secondary language

Language:English
Title:Steiner’s theorems on the complete quadrilateral
Abstract:
This paper discusses geometric object called complete quadrilateral and some of its proprieties. Complete quadrilateral is configuration, represented by four lines. These four lines are unparallel and intersect two by two at six points. Main emphasis of this paper will be on ten theorems, first presented by Jacob Steiner in 1828. The paper formulates and proves all ten theorems. It also derives couple of corollaries of the theorems. Apart from Steiner’s theorems a few basic geometric results and concepts are discussed, such as the ones of pole and polar, inversion, circle of nine points, Menelaus’s theorem, which are needed for proving Steiner’s theorems.

Keywords:complete quadrilateral, Miquel point, direct similtude, polar, Simson line

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