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Statements

Subject Item
n2:RIV%2F60076658%3A12410%2F08%3A00010626%21RIV10-MSM-12410___
rdf:type
skos:Concept n17:Vysledek
dcterms:description
The paper deals with properties of pentagons in a plane which are related to the area of a pentagon. First the formulas of Gauss and Monge holding for any pentagon in a plane are studied. Both formulas are derived by the theory of automated theorem proving. In the next part the area of cyclic pentagons is investigated. On the base of the Nagy-Rédey theorem and other results, the formula for the area of a cyclic pentagon which is given by its side lengths is rediscovered. This is the analogue of well-known Heron and Brahmagupta formulas for triangles and cyclic quadrilaterals. The method presented here could serve as a tool for solving this problem for cyclic n-gons for a higher n. The paper deals with properties of pentagons in a plane which are related to the area of a pentagon. First the formulas of Gauss and Monge holding for any pentagon in a plane are studied. Both formulas are derived by the theory of automated theorem proving. In the next part the area of cyclic pentagons is investigated. On the base of the Nagy-Rédey theorem and other results, the formula for the area of a cyclic pentagon which is given by its side lengths is rediscovered. This is the analogue of well-known Heron and Brahmagupta formulas for triangles and cyclic quadrilaterals. The method presented here could serve as a tool for solving this problem for cyclic n-gons for a higher n.
dcterms:title
Computation with Pentagons Computation with Pentagons
skos:prefLabel
Computation with Pentagons Computation with Pentagons
skos:notation
RIV/60076658:12410/08:00010626!RIV10-MSM-12410___
n4:aktivita
n10:V
n4:aktivity
V
n4:cisloPeriodika
x
n4:dodaniDat
n8:2010
n4:domaciTvurceVysledku
n14:6370950
n4:druhVysledku
n16:J
n4:duvernostUdaju
n11:S
n4:entitaPredkladatele
n15:predkladatel
n4:idSjednocenehoVysledku
360852
n4:idVysledku
RIV/60076658:12410/08:00010626
n4:jazykVysledku
n12:eng
n4:klicovaSlova
Area of a cyclic pentagon; Monge formula; Gauss formula; Groebner bases of ideals
n4:klicoveSlovo
n5:Gauss%20formula n5:Monge%20formula n5:Groebner%20bases%20of%20ideals n5:Area%20of%20a%20cyclic%20pentagon
n4:kodStatuVydavatele
DE - Spolková republika Německo
n4:kontrolniKodProRIV
[027EDA9B27AE]
n4:nazevZdroje
Journal for Geometry and Graphics
n4:obor
n13:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:rokUplatneniVysledku
n8:2008
n4:svazekPeriodika
12
n4:tvurceVysledku
Pech, Pavel
s:issn
1433-8157
s:numberOfPages
10
n3:organizacniJednotka
12410