Geodesic
Finding the Middle Ground Bisectors in p-Geometry
Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 23-32.

Voir la notice de l'article provenant de la source Heldermann Verlag

Bisectors of line segments are quite simple geometrical objects. Despite their simplicity, they have many surprising and useful properties. As metric objects, the shape of bisectors depends upon the metric considered. This article discusses geometric properties of bisectors of line segments in the plane, when the bisectors are taken with respect to the usual p-norms. Although the shape of bisectors changes as their defining p-norm varies, it is shown that the bisectors share exactly three points (or infinitely many points in exceptional cases determined by the orientation of the base line segment).
Classification : 51M05, 51B20
Mots-clés : Taxicab norm, p-bisector, p-norm 
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C. Bosch; M. Cabo; N. Charalambous; C. L. Garc�a; C. G�mez-Wulschner; G. Pastor; A. Reyes . Finding the Middle Ground Bisectors in p-Geometry. Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 23-32. http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a2/