A Spatial Generalization of Wallace–Simson Theorem on Four Lines
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F21%3A43903783" target="_blank" >RIV/60076658:12410/21:43903783 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-63403-2_10" target="_blank" >http://dx.doi.org/10.1007/978-3-030-63403-2_10</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-63403-2_10" target="_blank" >10.1007/978-3-030-63403-2_10</a>
Alternative languages
Result language
angličtina
Original language name
A Spatial Generalization of Wallace–Simson Theorem on Four Lines
Original language description
Motivation to this problem arose from the Wallace–Simson theorem which states, that feet of perpendiculars from a point P to three lines are collinear if and only if the point P belongs to the circumcircle of the triangle given by these three lines. 3D generalization of the Wallace–Simson theorem might be as follows: Determine the locus of the point P such that feet of normals from P to four arbitrary straight lines in three dimensional Euclidean space are coplanar. In this text we investigate a special case of straight lines being parallel to a fixed plane. We will show how to transfer this case to the planar one. Finally, we state a theorem, which is a generalization of the Wallace–Simson theorem in plane.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics
ISBN
978-3-030-63402-5
ISSN
2194-5357
e-ISSN
2194-5365
Number of pages
12
Pages from-to
103-114
Publisher name
Springer, Cham
Place of publication
Springer, Cham
Event location
Sao Paulo
Event date
Aug 9, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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