Geodesic
Steiner mapping of three points on Euclidean plane
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 20-26

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For Euclidean plane $\mathbb{C}$ we consider the Steiner mapping associating any three points $a, b, c$ with their median $s$ and the corresponding operator $P_D$ of metric projection of the space $l_1^3(\mathbb{C})$ onto its diagonal subspace $D=\{(x, x, x) \colon x \in \mathbb{C}\}$, $P_D(a, b, c)=(s, s, s) \colon s$. The exact value of the linearity coefficient of $P_D$ is calculated. 
@article{VMUMM_2018_1_a2,
     author = {K. V. Chesnokova},
     title = {Steiner mapping of three points on {Euclidean} plane},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {20--26},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a2/}
}
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K. V. Chesnokova. Steiner mapping of three points on Euclidean plane. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 20-26. http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a2/