A CHARACTERISATION OF EUCLIDEAN NORMED PLANES VIA BISECTORS
2018 ◽
Vol 99
(1)
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pp. 121-129
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Our main result states that whenever we have a non-Euclidean norm $\Vert \cdot \Vert$ on a two-dimensional vector space $X$, there exists some $x\neq 0$ such that for every $\unicode[STIX]{x1D706}\neq 1$, $\unicode[STIX]{x1D706}>0$, there exist $y,z\in X$ satisfying $\Vert y\Vert =\unicode[STIX]{x1D706}\Vert x\Vert$, $z\neq 0$ and $z$ belongs to the bisectors $B(-x,x)$ and $B(-y,y)$. We also give several results about the geometry of the unit sphere of strictly convex planes.
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2019 ◽
Vol 19
(05)
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pp. 2050086
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Keyword(s):
2011 ◽
Vol 85
(1)
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pp. 19-25
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