Extension of Simson--Wallace theorem on skew quadrilaterals and further properties

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F15%3A43889533" target="_blank" >RIV/60076658:12410/15:43889533 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-21362-0_7" target="_blank" >http://dx.doi.org/10.1007/978-3-319-21362-0_7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-21362-0_7" target="_blank" >10.1007/978-3-319-21362-0_7</a>

Result language
angličtina
Original language name
Extension of Simson--Wallace theorem on skew quadrilaterals and further properties
Original language description
The paper deals with the extension of the well-known Simson-Wallace theorem on skew quadrilaterals in E3. We investigate locus of a point P whose orthogonal projections K,L,M,N onto the sides of a skew quadrilateral form a tetrahedron of a constant volume s. It is shown that the locus is a cubic surface G. Further, some special cases of the locus for s=0 are described, where the cubic surface is decomposed into a plane and a one-sheet hyperboloid or into three planes. The conjecture is stated that thesecases are the only cases of reducibility of G.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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