Abstract
We prove that two strictly convex bodies in the plane subtending the same angles at each of the points of two parallel straight lines and a big closed curve, must coincide.
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Falconer, K. J.: X-ray problems for point sources, Proc. London Math. Soc. 46 (1983), 241–262.
Gardner, R. J. and McMullen, P.: On Hammer's X-ray problem, J. London Math. Soc. 21 (1980), 171–175.
Green, J. W.: Sets subtending a constant angle on a circle, Duke Math. J. 17 (1950), 263–267.
Kincses, J. and Kurusa, Á.: Can you recognize the shape of a figure from its shadows?, Contribution to Algebra and Geometry 36 (1995), 25–35.
Kurusa, Á.: You can recognize the shape of a figure from its shadows!, Geom. Dedicata 59 (1996), 113–125.
Nietsche, J. C. C.: Isotropic characterization of a circle (Proof of a conjecture of M. S. Klamkin), Amer Math. Monthly 97 (1990), 45–47.
Santaló, L. A.: Integral Geometry and Geometric Probability, Addison-Wesley, New York, 1976.
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Supported by the Hungarian NSF, OTKA Nr. T4427, W015425 and F016226.
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Kurusa, Á. The shadow picture problem for nonintersecting curves. Geom Dedicata 59, 103–112 (1996). https://doi.org/10.1007/BF00181528
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DOI: https://doi.org/10.1007/BF00181528