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Kompleksna števila v geometriji : magistrsko delo
ID Grafenauer, Olivija (Author), ID Kuzman, Uroš (Mentor) More about this mentor... This link opens in a new window

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Abstract
V magistrski nalogi s pomočjo kompleksnih števil obravnavam nekatere geometrijske izreke. V prvem delu naloge predstavim kompleksno interpretacijo osnovnih geometrijskih pojmov, ki jih nato uporabim pri dokazovanju nekaterih klasičnih geometrijskih izrekov, kot so Cliffordovi izreki, izrek o obstoju krožnice devetih točk, izrek o Simsonovi premici in Simsonov izrek za štirikotnike, Cantorjevi izreki, Feuerbachov izrek, Morleyev izrek. Nalogo zaključim z novejšim rezultatom, ki je bil dokazan šele leta 2001 - kompleksnim Descartesovim izrekom.

Language:Slovenian
Keywords:kompleksna števila, geometrija, kompleksni Descartesov izrek
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
PID:20.500.12556/RUL-112857 This link opens in a new window
UDC:514
COBISS.SI-ID:18807897 This link opens in a new window
Publication date in RUL:16.11.2019
Views:1643
Downloads:270
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Secondary language

Language:English
Title:Complex numbers in geometry
Abstract:
In my masters thesis I consider some geometric theorems with the help of complex numbers. The thesis consists of complex interpretation of some of the basic geometric terms, with the help of which I consider a set of geometric theorems, such as the Clifford theorems, the nine point circle theorem, the Simsons line theorem and its generalization for quadrilaterals, the Cantor theorems, the Feuerbach theorem, the Morley theorem. Finally, I consider a result that has been proven in the year 2001 - the complex Descartes theorem.

Keywords:complex numbers, geometry, complex Descartes theorem

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