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You can recognize the shape of a figure from its shadows!

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Abstract

Let C 1 and C 2 be convex closed domains in the plane with C 2 boundaries ∂C 1 and ∂C 2 intersecting each other in nonzero angles. Assume the two strictly convex bodies F 1 and F 2 with C 2 boundaries in the interior of C 1∩C 2 subtend equal visual angles at each point of ∂C 1 and ∂C 2. Then F 1 and F 2 coincide. Generalizations are also discussed.

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Authors and Affiliations

  1. Bolyai Institute, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    Árpád Kurusa

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  1. Árpád Kurusa
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Supported by the Hungarian NSF, OTKA Nr. T4427, W015425 and F016226.

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Kurusa, Á. You can recognize the shape of a figure from its shadows!. Geom Dedicata 59, 113–125 (1996). https://doi.org/10.1007/BF00155723

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  • DOI: https://doi.org/10.1007/BF00155723

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