On One Locus in the Plane

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F19%3A43898282" target="_blank" >RIV/60076658:12410/19:43898282 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-95588-9_14" target="_blank" >http://dx.doi.org/10.1007/978-3-319-95588-9_14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-95588-9_14" target="_blank" >10.1007/978-3-319-95588-9_14</a>

Result language
angličtina
Original language name
On One Locus in the Plane
Original language description
In this work we deal with the problem: determine the locus of the point P such that the feet of the perpendiculars from P to (extended) sides of a given planar quadrilateral ABCD are concyclic. In general the locus is a cubic curve. We get a correspondence between some types of quadrilaterals and some classes of cubic curves. In the paper we answer several questions: For which quadrilaterals is the searched locus a cubic curve and for which a conic? What are properties of the cubic? For which quadrilaterals is the cubic decomposable? Which quadrilaterals correspond to singular cubic curves? What happens if a quadrilateral is tangential?
Czech name
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Czech description
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Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
ICGG 2018-Proceedings of the Conference on Geometry and Graphics
ISBN
978-3-319-95587-2
ISSN
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e-ISSN
neuvedeno
Number of pages
13
Pages from-to
184-196
Publisher name
Springer International Publishing
Place of publication
Cham
Event location
Milano
Event date
Aug 3, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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