A visit to taxicab geometry

• Autores: J. R. Hanson
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 43, Nº. 8, 2012, págs. 1109-1123
• Idioma: inglés
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• Resumen

  • The taxi metric is introduced, compared to the Euclidean metric, and used to define the taxi circle. For all pairs of points Aand Bthe set of points equally distant under the taxi metric to Aand to Bis 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 Pto a line lis shown to be the shorter of the vertical distance from Pto lor the horizontal distance from Pto 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.