id: 05915541
dt: a
an: 05915541
au: Pech, Pavel
ti: On equivalence of conditions for a quadrilateral to be cyclic.
so: Murgante, Beniamino (ed.) et al., Computational science and its
    applications ‒ ICCSA 2011. International conference, Santander,
    Spain, June 20‒23, 2011. Proceedings, Part IV. Berlin: Springer (ISBN
    978-3-642-21897-2/pbk). Lecture Notes in Computer Science 6785, 399-411
    (2011).
py: 2011
pu: Berlin: Springer
la: EN
cc: 
ut: cyclic quadrilaterals; Ptolemy inequality; automated geometry theorem
    proving
ci: 
li: doi:10.1007/978-3-642-21898-9_34
ab: Summary: In the paper we will prove a theorem that puts together three
    conditions ‒ Ptolemy, Cubic and Quartic ‒ for a convex
    quadrilateral to be cyclic. Further Ptolemy inequality is proved. 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 Ptolemy conditions. 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.
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