Journal for Geometry and Graphics 20 (2016), No. 1, 023--032
Copyright Heldermann Verlag 2016
Finding the Middle Ground Bisectors in p-Geometry
Carlos Bosch
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
bosch@itam.mx
Marta Cabo
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
Nelia Charalambous
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
César L. García
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
Claudia Gómez-Wulschner
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
Guillermo Pastor
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
Araceli Reyes
Dep. de Matemáticas, Instituto Tecnológico Autónomo, Rio Hondo #1, Col. Tizapán - San Angel, 01080 México, México
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).
Keywords: Taxicab norm, p-bisector, p-norm.
MSC: 51M05; 51B20
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