Computation with Pentagons

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F08%3A00010626" target="_blank" >RIV/60076658:12410/08:00010626 - 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

Computation with Pentagons

Original language 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Publication year

2008

Confidentiality

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

Name of the periodical

Journal for Geometry and Graphics

ISSN

1433-8157

e-ISSN

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Volume of the periodical

12

Issue of the periodical within the volume

x

Country of publishing house

DE - GERMANY

Number of pages

10

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

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