Wallace–Simson Theorem on Four Lines Parallel to a Plane

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/60076658:12410/23:43906338

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Wallace–Simson Theorem on Four Lines Parallel to a Plane

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Wallace–Simson Theorem on Four Lines Parallel to a Plane

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

—

Svazek periodika

78

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

11

Strana od-do

—

Kód UT WoS článku

001022882500003

EID výsledku v databázi Scopus

2-s2.0-85164152640