Geodesic
Normed spaces in which the unit sphere has no bias
Matematičeskie zametki, Tome 7 (1970) no. 3, pp. 307-310 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find the class of normed spaces in which the unit sphere has no bias (the midpoint of the segment joining two arbitrary normalized elements is, among the points of this segment, the one nearest to the zero element). 
@article{MZM_1970_7_3_a6,
     author = {N. I. Gurarii and Yu. I. Sozonov},
     title = {Normed spaces in which the unit sphere has no bias},
     journal = {Matemati\v{c}eskie zametki},
     pages = {307--310},
     year = {1970},
     volume = {7},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_3_a6/}
}
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N. I. Gurarii; Yu. I. Sozonov. Normed spaces in which the unit sphere has no bias. Matematičeskie zametki, Tome 7 (1970) no. 3, pp. 307-310. http://geodesic.mathdoc.fr/item/MZM_1970_7_3_a6/