Properties of Tangential and Cyclic Polygons: An Application of Circulant Matrices

Autor/inn/en	Leung, Allen; Lopez-Real, Francis
Titel	Properties of Tangential and Cyclic Polygons: An Application of Circulant Matrices
Quelle	In: International Journal of Mathematical Education in Science and Technology, 34 (2003) 6, S.859-870 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Geometry; Matrices; Equations (Mathematics); Geometric Concepts; Validity; Mathematical Logic; Problem Solving + Suchen Sie Ihr Suchwort? Geometrie; Matrizenrechnung; Equations; Mathematics; Gleichungslehre; Elementare Geometrie; Gültigkeit; Mathematical logics; Mathematische Logik; Problemlösen
Abstract	In 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 P[subscript n] with n even is slippable (or conformable) and the sum of a set of non-adjacent sides (or interior angles) of P[subscript n] satisfies certain equalities. On the other hand, for a tangential (or cyclic) polygon P[subscript n] with n odd, it is rigid and the sum of a set of non-adjacent sides (or interior angles) of P[subscript n] 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. (Contains 5 figures.) (Author).
Anmerkungen	Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10