On Equivalence of Conditions for a Quadrilateral to Be Cyclic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F11%3A43882714" target="_blank" >RIV/60076658:12410/11:43882714 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On Equivalence of Conditions for a Quadrilateral to Be Cyclic
Original language description
In the paper we will prove a theorem that puts together three conditions - Ptolemy, Cubic and Quartic - for a convex quadrilateral to be cyclic. Some related formulas from geometry of polygons are derived as well. These computations were done by the theory of automated geometry theorem proving using Gröbner bases approach. Dynamic geometry system GeoGebra was applied to verify Ptolemyconditions. These conditions were subsequently proved by Wu-Ritt method using characteristic sets. The novelty of the paper is the method of proving geometric inequalities. Also some relations among Ptolemy, Cubic and Quartic conditions seem to be new.
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
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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