Geodesic
Convex Bodies of Constant Width and the Apollonian Metric
Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 2
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The study of constant width sets goes at least as far back as the time of Euler. The Apollonian metric, on the other hand, is a relatively new concept. It was introduced by Beardon in
Classification : Primary 30F45, Secondary 52A20. 
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     author = {Marina Borovikova and Zair Ibragimov},
     title = {Convex {Bodies} of {Constant} {Width} and the {Apollonian} {Metric}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2008},
     volume = {31},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2008_31_2_a0/}
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Marina Borovikova; Zair Ibragimov. Convex Bodies of Constant Width and the Apollonian Metric. Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2008_31_2_a0/