RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2003 Volume 299, Pages 87–108 (Mi znsl1034)

This article is cited in 2 papers

Shortest inspection curves for a sphere

V. A. Zalgaller


Abstract: What is the form of the shortest curve $C$ going outside the unit sphere $S$ in $\mathbb R^3$ such that passing along $C$ we can see all points of $S$ from outside? How will the form of $C$ change if we require that $C$ have one of its (or both) endpoints on $S$? A solution to the latter problem also answers the following question. You are in a half-space at a unit distance from the boundary plane $P$, but do not know where $P$ is. What is the shortest space curve $C$ such that going along $C$ you certainly will come to $P$? Geometric arguments are given suggesting that the required curves should be looked for in certain classes depending on several parameters. A computer analysis yields the best curves in the classes. Some other questions are solved in a similar way.

UDC: 514.177.2+517.977.5

Received: 25.12.2001


 English version:
Journal of Mathematical Sciences (New York), 2005, 131:1, 5307–5321

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025