Wallace–Simson Theorem on Four Lines Parallel to a Plane
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00012039" target="_blank" >RIV/46747885:24510/23:00012039 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12410/23:43906338
Result on the web
<a href="https://link.springer.com/article/10.1007/s00025-023-01950-2" target="_blank" >https://link.springer.com/article/10.1007/s00025-023-01950-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-023-01950-2" target="_blank" >10.1007/s00025-023-01950-2</a>
Alternative languages
Result language
angličtina
Original language name
Wallace–Simson Theorem on Four Lines Parallel to a Plane
Original language description
The impulse to study this topic came from a variant of the Wallace-Simson theorem, which deals with the locus of the point P such that the points that are symmetric to P with respect to three lines in the plane are collinear. A 3D generalization can be as follows: Given four straight lines which are parallel to a plane. Determine the locus of the point P such that points that are symmetric to P with respect to these four lines are coplanar. Surprisingly, the locus of P is a cylinder of revolution with the axis which is perpendicular to the fixed plane. Moreover, all planes given by points that are symmetric with an arbitrary point P of the locus with respect to the given four lines pass through a fixed line f. While in the planar version the fixed element is the orthocenter of the triangle given by the three lines, the role of the fixed line f with respect to the four given lines is not obvious.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
—
Volume of the periodical
78
Issue of the periodical within the volume
5
Country of publishing house
CH - SWITZERLAND
Number of pages
11
Pages from-to
—
UT code for WoS article
001022882500003
EID of the result in the Scopus database
2-s2.0-85164152640