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Lassak, M., Covering a plane convex body by four homothetical copies with the smallest positive ratio, Geom. Dedicata 21 (1986), 157-167. MR 88c :52013 Covering a plane convex body by

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Boltyanski, V. , A problem on the illumination of the boundary of a convex body (in Russian). Izv. Mold. Fil. Akad. Nauk SSSR (1960), no. 10, 77–84. MR 2006f :52003 Boltyanski, V. , A

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. 1938 7 121 142 Averkov, G. , On boundary arcs joining antipodal points of a planar convex body

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Summary  

The notion of successive illumination parameters of convex bodies is introduced. We prove some theorems in the plane and determine the exact values of the successive illumination parameters of spheres, cubes and cross-polytopes for some dimensions.

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Groemer, H. , Stability results for convex bodies and related spherical integral transformations, Adv. Math. , 109 (1994), no. 1, 45–74. MR 95j :52005 Groemer H

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Abstract  

Every sequence of positive homothetic copies of a planar convex body C whose total area does not exceed a quarter of the area of C can be translatively packed in C.

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. Theorie der konvexen Körper. Berichtigter Reprint 1974 Hammer, P. C. , Diameters of convex bodies, Proc. Amer

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29 40 Lassak, M., On five points in a plane convex body in at least unit relative distances,in: Coll. Math. Soc. János Bolyai 63 Intuitive Geometry, Szeged (1991), 245

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Bambah, R. P. , Polar reciprocal convex bodies, Proc. Cambr. Phil. Soc. , 51 (1955), 377–378. MR 16 , 1145 Bambah R. P. Polar reciprocal convex bodies

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. Differential Geom ., 26 ( 1987 ), 285 – 314 . [25] H ammer , P. C. , Convex bodies associated with a convex body , Proc. Amer. Math. Soc ., 2 ( 1951 ), 781 – 793

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