A translation of Zalgaller's "The shortest space curve of unit width" (1994)

2019/10/07 by Steven Finch, Steven R. Finch, Finch, Steven
Computer Science · Mathematics · #49Nxx (Primary) 51M16 #52A40 #65K15 (Secondary) #Digital Image Processing Techniques #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.HO #math.MG #msc:49Nxx #msc:51M16 #msc:52A40 #msc:65K15

paper · pdf · doi:10.48550/arxiv.1910.02729

11 pages, 9 figures

arxiv created 2019/10/07 · openalex publication_date 2019/10/07 · arxiv updated 2019/10/08 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

This is an English translation of V. A. Zalgaller's article "On a problem of the shortest space curve of unit width" that appeared in Matematicheskaya Fizika, Analiz, Geometriya v. 1 (1994) n. 3--4, 454--461. We refer interested readers to Ghomi (2018) for up-to-date discussion; the curve L₃ of length 3.9215... in Zalgaller (1994) still appears to be shortest, whereas the closed curve L₅ is provably not of unit width. I am thankful to Natalya Pluzhnikov for her dedicated work and to the B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine for permission to post this translation on the arXiv.

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