<div class="csl-bib-body">
<div class="csl-entry">Stachel, H. (2022). On the Diagonals of Billiards. In <i>ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics</i> (pp. 19–33). https://doi.org/10.1007/978-3-031-13588-0_2</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/136175
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dc.description.abstract
A billiard is the trajectory of a mass point in a domain with ideal physical reflections in the boundary e. If e is an ellipse, then the billiard’s sides are tangents of a confocal conic called caustic c. The variation of billiards in e with caustic c is called billiard motion. We recall and extend a classical result of Poncelet on the diagonals of billiards which envelope motion-invariant conics. Each billiard in e with caustic c is the flat pose of a Henrici framework. Its spatial poses define focal billiards in an ellipsoid with a fixed focal conic c. We prove that for even j the j-th diagonals are located on a motion-invariant one-sheeted hyperboloid.
en
dc.language.iso
en
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dc.relation.ispartofseries
Lecture Notes on Data Engineering and Communications Technologies
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dc.subject
Billiard
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dc.subject
Caustic
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dc.subject
Ellipse
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dc.subject
Focal billiard
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dc.subject
Poncelet grid
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dc.title
On the Diagonals of Billiards
en
dc.type
Inproceedings
en
dc.type
Konferenzbeitrag
de
dc.relation.isbn
978-3-031-13588-0
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dc.description.startpage
19
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dc.description.endpage
33
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dc.type.category
Full-Paper Contribution
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tuw.booktitle
ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics
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tuw.container.volume
146
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tuw.peerreviewed
true
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tuw.researchTopic.id
C1
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tuw.researchTopic.name
Computational Materials Science
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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tuw.publisher.doi
10.1007/978-3-031-13588-0_2
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dc.description.numberOfPages
15
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tuw.author.orcid
0000-0001-5300-4978
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tuw.event.name
20th International Conference on Geometry and Graphics (ICGG 2022)
en
tuw.event.startdate
15-08-2022
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tuw.event.enddate
19-08-2022
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Sao Paulo
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tuw.event.country
BR
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tuw.event.presenter
Stachel, Hellmuth
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.openairetype
Inproceedings
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item.openairetype
Konferenzbeitrag
-
item.grantfulltext
none
-
item.cerifentitytype
Publications
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.fulltext
no Fulltext
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
