Dark Clouds on Spheres and Totally Non-spherical Bodies of Constant Breadth
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چکیده
In this paper, we show that for any dimension d ≥ 3 there exists a body of constant breadth C, such that its projection onto any 2-plane is non-spherical. We call such a body totally non-spherical. The circumradius of the projection of any totally non-spherical body C of constant breadth onto any 2-plane is bigger than the half diameter of C. Showing the existence of such a body extends results of Eggleston [4] and Weissbach [2], who showed it in the case d = 3.
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تاریخ انتشار 2003