Planar rectifiable curves are determined by their projections |
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Authors: | T J Richardson |
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Institution: | (1) AT&T Bell Laboratories, Room 2C-370, 07974 Murray Hill, NJ, USA |
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Abstract: | In 1954 Steinhaus raised the question of whether a rectifiable curve is characterized by its projections. A projection onto
a lineG at the pointp counts the number of points in the set which lie on the line which is perpendicular toG and passes throughp. We prove this is so, and give a method to reconstruct a closed connected rectifiable set from its projections. |
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