A Visit to Taxicab Geometry

Autor/in	Hanson, J. R.
Titel	A Visit to Taxicab Geometry
Quelle	In: International Journal of Mathematical Education in Science and Technology, 43 (2012) 8, S.1109-1123 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2012.662291
Schlagwörter	Geometric Concepts; Mathematics Instruction; Mathematics Education; Geometry; Plane Geometry + Suchen Sie Ihr Suchwort? Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Mathematische Bildung; Geometrie; Planimetrie
Abstract	The taxi metric is introduced, compared to the Euclidean metric, and used to define the taxi circle. For all pairs of points "A" and "B" the set of points equally distant under the taxi metric to "A" and to "B" is determined. For any triangle these sets are used to either find the centre of a taxi circle that can circumscribe the triangle or to show that there is no taxi circle that can circumscribe the triangle. The taxi distance from a point "P" to a line "l" is shown to be the shorter of the vertical distance from "P" to "l" or the horizontal distance from "P" to "l". It is shown that ratios of Euclidean lengths of segments that are collinear or that lie on parallel lines equal the corresponding taxi ratios of the same segments. Using this property, a method to construct the taxi bisector of any angle is demonstrated. For any triangle the intersection of any two taxi angle bisectors gives the centre of the inscribed taxi circle for the triangle. (Contains 20 figures.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10