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Article: Properties of tangential and cyclic polygons: an application of circulant matrices

TitleProperties of tangential and cyclic polygons: an application of circulant matrices
Authors
KeywordsMathematics
Issue Date2003
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/0020739X.asp
Citation
International Journal of Mathematical Education in Science and Technology, 2003, v. 34 n. 6, p. 859-870 How to Cite?
AbstractIn this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon Pn with n even is slippable (or conformable) and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain equalities. On the other hand, for a tangential (or cyclic) polygon Pn with n odd, it is rigid and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain inequalities. These inequalities give a definite answer to the question raised by Lopez-Real concerning the alternating sum of interior angles of a cyclic polygon.
Persistent Identifierhttp://hdl.handle.net/10722/48569
ISSN
2015 SCImago Journal Rankings: 0.365

 

DC FieldValueLanguage
dc.contributor.authorLeung, AYLen_HK
dc.contributor.authorLopez-Real, FJen_HK
dc.date.accessioned2008-05-22T04:17:26Z-
dc.date.available2008-05-22T04:17:26Z-
dc.date.issued2003en_HK
dc.identifier.citationInternational Journal of Mathematical Education in Science and Technology, 2003, v. 34 n. 6, p. 859-870en_HK
dc.identifier.issn0020-739Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/48569-
dc.description.abstractIn this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon Pn with n even is slippable (or conformable) and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain equalities. On the other hand, for a tangential (or cyclic) polygon Pn with n odd, it is rigid and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain inequalities. These inequalities give a definite answer to the question raised by Lopez-Real concerning the alternating sum of interior angles of a cyclic polygon.en_HK
dc.format.extent144916 bytes-
dc.format.extent7292240 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeimage/jpeg-
dc.languageengen_HK
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/0020739X.aspen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectMathematicsen_HK
dc.titleProperties of tangential and cyclic polygons: an application of circulant matricesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0020-739X&volume=34&issue=6&spage=859&epage=870&date=2003&atitle=Properties+of+tangential+and+cyclic+polygons:+an+application+of+circulant+matrices+en_HK
dc.identifier.emailLeung, AYL: aylleung@hkucc.hku.hken_HK
dc.identifier.emailLopez-Real, FJ: lopezfj@hkucc.hku.hken_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1080/00207390310001595456en_HK
dc.identifier.hkuros89679-

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