On the nine-point conic of hyperbolic triangles

A tétel rövid nézete
dc.contributor.authorSzilasi, Zoltán
dc.date.accessioned2025-12-04T19:46:49Z
dc.date.available2025-12-04T19:46:49Z
dc.date.issued2025-12-01
dc.description.abstractIn the Cayley–Klein model, we review some basic results concerning the geometry of hyperbolic triangles. We introduce a new definition of the circumcircle of a hyperbolic triangle, guaranteed to exist in every case, and describe its main properties. Our central theorem establishes, by means of purely elementary projective geometric arguments, that a hyperbolic triangle has a nine-point conic if and only if it is a right triangle. Subject Classification: 51M09en
dc.formatapplication/pdf
dc.identifier.citationTeaching Mathematics and Computer Science, Vol. 23 No. 2 (2025) , 195-211
dc.identifier.doihttps://doi.org/10.5485/TMCS.2025.15646
dc.identifier.eissn2676-8364
dc.identifier.issn1589-7389
dc.identifier.issue2
dc.identifier.jatitleTeach. Math. Comp. Sci.
dc.identifier.jtitleTeaching Mathematics and Computer Science
dc.identifier.urihttps://hdl.handle.net/2437/399463
dc.identifier.volume23
dc.languageen
dc.relationhttps://ojs.lib.unideb.hu/tmcs/article/view/15646
dc.rights.accessOpen Access
dc.rights.ownerZoltán Szilasi
dc.subjectCayley-Klein planeen
dc.subjecthyperbolic trianglesen
dc.subjectFeuerbach circleen
dc.subjecteleven-point conicen
dc.titleOn the nine-point conic of hyperbolic trianglesen
dc.typefolyóiratcikkhu
dc.typearticleen
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Teaching Mathematics and Computer Science (DE-journals)