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Title:Tretji thébaultov problem : magistrsko delo
Authors:ID Vohar, Matej (Author)
ID Hvala, Bojan (Mentor) More about this mentor... New window
Files:.pdf EMAG_Vohar_Matej_2022.pdf (2,50 MB)
MD5: E05E55F8332AFA54A2E32FA369514934
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
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 pa ni dokazal on. V magistrski nalogi sta predstavljena dva različna dokaza tega izreka. Za konec so predstavljene še nekatere z izrekom povezane zanimivosti.
Keywords:Geometrija trikotnika, Thebaultov izrek, Paposov izrek, posplošeni Ptolomejev izrek, Miquelov izrek, ortogonalne krožnice, potenčne premice.
Place of publishing:Maribor
Place of performance:Maribor
Publisher:[M. Vohar]
Year of publishing:2022
Number of pages:60 f.
PID:20.500.12556/DKUM-82363 New window
UDC:514.112.3(043.2)
COBISS.SI-ID:127479043 New window
Publication date in DKUM:28.10.2022
Views:881
Downloads:78
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Licences

License:CC BY-SA 4.0, Creative Commons Attribution-ShareAlike 4.0 International
Link:http://creativecommons.org/licenses/by-sa/4.0/
Description:This Creative Commons license is very similar to the regular Attribution license, but requires the release of all derivative works under this same license.
Licensing start date:17.08.2022

Secondary language

Language:English
Title:Thébault's problem iii : na študijskem programu 2. stopnje Matematika
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.
Keywords:Triangle geometry, Thebault's theorem, Papos theorem, general Ptolemy theorem, Miquel theorem, ortogonal circles, radical axes.


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