On Equivalence of Conditions for a Quadrilateral to Be Cyclic

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On Equivalence of Conditions for a Quadrilateral to Be Cyclic

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Equivalence of Conditions for a Quadrilateral to Be Cyclic

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Lecture Notes in Computer Science

ISSN

0302-9743

e-ISSN

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Svazek periodika

6785

Číslo periodika v rámci svazku

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Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

399-411

Kód UT WoS článku

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EID výsledku v databázi Scopus

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