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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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