On Reuleaux Triangles in Minkowski Planes
نویسندگان
چکیده
In this paper we prove some results on Reuleaux triangles in (Minkowski or) normed planes. For example, we reprove Wernicke’s result (see [21]) that the unit disc and Reuleaux triangles in a normed plane are homothets if and only if the unit circle is either an affine regular hexagon or a parallelogram. Also we show that the ratio of the area of the unit ball of a Minkowski plane to that of a Reuleaux triangle of Minkowski width 1 lies between 4 and 6. The Minkowskian analogue of Barbier’s theorem is obtained, and some inequalities on areas of Reuleaux triangles are given. MSC 2000: 52A10, 52A40, 46B20, 46B04
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