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dc.contributor.author
Hungerbühler, Norbert
dc.contributor.author
Pohle, Clemens
dc.date.accessioned
2020-11-02T08:43:09Z
dc.date.available
2020-10-30T13:56:12Z
dc.date.available
2020-11-02T08:43:09Z
dc.date.issued
2020-10
dc.identifier.uri
http://hdl.handle.net/20.500.11850/448867
dc.description.abstract
Suppose there are n harmonic pencils of lines given in the plane. We are interested in the question whether certain triples of these lines are concurrent or if triples of intersection points of these lines are collinear, provided that we impose suitable conditions on the initial harmonic pencils. Such conditions can be that certain of the given lines coincide, are concurrent or that certain intersection points are collinear. The study of these questions for n = 2, 3, 4 sheds light on some well known affine configurations and provides new results in the projective setting. As applications, we will formulate generalizations or stronger versions of the theorems of Pappus, Desargues, Ceva and Menelaos. Notably, the generalized theorems of Ceva and Menelaos suggest a new way to generalize the terms ‘collinearity’ and ‘concurrency’.
en_US
dc.language.iso
en
en_US
dc.publisher
Vasile Alecsandri National College of Bacau
en_US
dc.subject
Harmonic pencils
en_US
dc.subject
Theorems of Pappus
en_US
dc.subject
Desargues
en_US
dc.subject
Ceva and Menelaos
en_US
dc.title
Communicating harmonic pencils of lines
en_US
dc.type
Journal Article
ethz.journal.title
International Journal of Geometry
ethz.journal.volume
9
en_US
ethz.journal.issue
2
en_US
ethz.pages.start
15
en_US
ethz.pages.end
38
en_US
ethz.publication.place
Bacau
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
en_US
ethz.identifier.url
https://ijgeometry.com/product/norbert-hungerbuhler-and-clemens-pohle-communicating-harmonic-pencils-of-lines/
ethz.date.deposited
2020-10-30T14:02:40Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-11-02T08:43:21Z
ethz.rosetta.lastUpdated
2020-11-02T08:43:21Z
ethz.rosetta.versionExported
true
ethz.COinS
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