Orthocentral quadrilaterals and their properties

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F24%3A00012667" target="_blank" >RIV/46747885:24510/24:00012667 - isvavai.cz</a>

Alternative codes found

RIV/60076658:12410/24:43908241

Result on the web

<a href="https://link.springer.com/article/10.1007/s00022-024-00735-4" target="_blank" >https://link.springer.com/article/10.1007/s00022-024-00735-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00022-024-00735-4" target="_blank" >10.1007/s00022-024-00735-4</a>

Result language

angličtina

Original language name

Orthocentral quadrilaterals and their properties

Original language description

We start the article with already known theorem: Let a quadrilateral ABCD be given in the plane. Construct the orthocenters Ha,Hb, Hc, and Hd, of triangles BCD, ACD, ABD and ABC. Then the quadrilateral has the same area as the quadrilateral ABCD. In the paper, we give a synthetic proof of this theorem. In the framework of this proof we formulate another theorem, which is then generalized in various ways. Presented analytic proofs of these generalizations are based on Gröbner bases computation.

Czech name

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Czech description

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Type

J_imp - 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

2024

Confidentiality

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

Name of the periodical

Journal of Geometry

ISSN

0047-2468

e-ISSN

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Volume of the periodical

Volume 115

Issue of the periodical within the volume

September

Country of publishing house

CH - SWITZERLAND

Number of pages

11

Pages from-to

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UT code for WoS article

001318500700001

EID of the result in the Scopus database

2-s2.0-85204876119