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Observations on circumcenters in normed planesJussi V?is?l?Original PaperDOI:
10.-017-0338-6V?is?l?, J. Beitr Algebra Geom (2017). doi:10.-017-0338-6
We give a necessary and sufficient condition for the existence of a circumcenter of a triangle in a normed plane. We also give alternative proofs of some results in Alonso et al. (Comput Geom 45:350–369, ).Circumcenter Bisector Normed plane Alonso, J., Martini, H., Spirova, M.: Minimal enclosing discs, circumcircles, and circumcenters on normed planes (part II). Comput. Geom. 45, 350–369 (2012)Jahn, T., Spirova, M.: On bisectors in normed spaces. Contrib. Discrete Math. 10(2), 1–9 (2015)Kramer, H., Németh, A.B.: The application of Brouwer’s fixed point theorem of convex bodies (Romanian). An. Univ. Timisoara Ser. Sti. Mat. 13, 33–39 (1977)Martini, H., Swanepoel, K.J., Weiss, G.: The geometry of Minkowski spaces—a survey, part I. Expo. Math. 19, 97–142 (2001)Martini, H., Swanepoel, K.J.: The geometry of Minkowski spaces—a survey, part II. Expo. Math. 22, 93–144 (2004)Mayer, A.E.: Eine ?berkonvexit?t. Math. Z. 39, 511–531 (1935)Newman, M.H.A.: Elements of the Topology of Plane Sets of Points. Cambridge University Press, Cambridge (1961)Thompson, A.C.: Minkowski Geometry. Cambridge University Press, Cambridge (1996)Jussi V?is?l?11.Matematiikan laitosHelsingin yliopisto, PL 68HelsinkiFinland
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