Generalization of Simson–Wallace theorem: planar and spatial formulation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00012041" target="_blank" >RIV/46747885:24510/23:00012041 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12410/23:43905660
Result on the web
<a href="https://link.springer.com/article/10.1007/s00022-022-00665-z" target="_blank" >https://link.springer.com/article/10.1007/s00022-022-00665-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00022-022-00665-z" target="_blank" >10.1007/s00022-022-00665-z</a>

Result language
angličtina
Original language name
Generalization of Simson–Wallace theorem: planar and spatial formulation
Original language description
The paper studies a problem that represents a natural spatial generalization of the well-known Simson–Wallace theorem: Let four skew lines parallel to a fixed plane be given. Determine the locus of the point P in space so that the reflections of P in the given lines are coplanar. The result was very surprising for us — we get a cylinder of revolution. By orthogonal projection onto the given plane, the problem is reformulated as a planar one and subsequently solved synthetically. This solution turns out to have many properties in common with the classical Simson–Wallace theorem.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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