Tretji thébaultov problem

magistrsko delo

Matej Vohar (Author), Bojan Hvala (Mentor)

Abstract

Tretji Thébaultov izrek govori o trikotniku in treh posebnih krožnicah, katerih središča so kolinearna, veljata pa tudi dve razmerji med dolžinami daljic in tangensi kotov. Do te ugotovitve je prišel Victor Thebault, francoski matematik. Samega izreka ni dokazal on. V magistrskem delu sta predstavljena dva različna dokaza tega izreka. Za konec so predstavljene tudi nekatere z izrekom povezane zanimivosti.

Keywords

magistrska dela;geometrija trikotnika;Thebaultov izrek;Paposov izrek;posplošeni Ptolomejev izrek;Miquelov izrek;ortogonalne krožnice;potenčne premice;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Vohar]
UDC:	514.112.3(043.2)
COBISS:	127479043
Views:	12
Downloads:	4
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Thébault's problem iii
Secondary abstract:	Thébault's third theorem talks about a triangle and three special circles whose centres are collinear, and there are two relations between the lengths of the lines and the tangents of the angles. This conclusion was discovered by Victor Thebault, a French mathematician. However, he did not prove the theorem himself. This thesis presents two proofs of the theorem. Finally, some further curiosities in this context are presented.
Secondary keywords:	master theses;triangle geometry;Thebault's theorem;Papos theorem;general Ptolemy theorem;Miquel theorem;ortogonal circles;radical axes;Trikotnik;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	60 f.
ID:	16192892