Lost in a forest

American Mathematical Monthly

Volumn 111, Issue 8, 2004, Pages 645-654

  Finch, Steven R ^a,b,c   Wetzel, John E ^d  

^a MIT LINCOLN LABORATORY   (United States)

^b SALEM STATE UNIVERSITY   (United States)

^c Clay Mathematics Institute   (United States)

^d UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7944237791     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/4145038     Document Type: Article

References (47)

1. A. Adhikari and J. Pitman, The shortest planar arc of width 1, this MONTHLY 96 (1989) 309-327.
2. E. J. Anderson and S. P. Fekete, Two-dimensional rendezvous search, Oper. Res. 49 (2001) 107-118.
3. R. A. Baeza-Yates and R. Schott, Parallel searching in the plane, Comput. Geom. 5 (1995) 143-154.
4. R. A. Baeza-Yates, J. C. Culberson, and G. J. E. Rawlins, Searching in the plane, Inform. and Comput. 106 (1993) 234-252.
5. -, Searching with uncertainty (extended abstract), in Proceedings of the First Scandinavian Workshop on Algorithm Theory, R. Karlsson and A. Lingas, eds., Lecture Notes in Computer Science, no. 318, Springer-Verlag, Berlin, 1988, pp. 176-189.
6. R. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957.
7. -, Minimization problem, Bull. Amer. Math. Soc. 62 (1956) 270.
8. -, An optimal search, SIAM Review 5 (1963) 274.
9. R. Benson, Euclidean Geometry and Convexity, McGraw-Hill, New York, 1966.
10. G. Berzsenyi, Lost in a forest (a problem area initiated by the late Richard E. Bellman), Quantum (November/December, 1995) 41.
11. A. S. Besicovitch, On arcs that cannot be covered by an open equilateral triangle of side 1, Math. Gazette 49 (1965) 286-288.
12. H. T. Croft, K. J. Falconer, and R. K. Guy, Unsolved Problems in Geometry, Springer-Verlag, New York, 1991.
13. H. Eggleston, Convexity, Cambridge University Press, Cambridge, 1958.
14. V. Faber and J. Mycielski, The shortest curve that meets all lines that meet a convex body, this MONTHLY 93 (1986) 796-801.
15. S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003.
16. S. Gal, Search Games, Academic Press, New York, 1980.
17. B. Gluss, The minimax path in a search for a circle in a plane, Naval Res. Logist. Quart. 8 (1961) 357-360.
18. R. Graham, Problem 41, Proceedings, 1963 Number Theory Conference, University of Colorado, Boulder, 1963.
19. O. Gross, A Search Problem Due to Bellman, U. S. Air Force Project Rand Research Memorandum RM-1603, Rand Corporation, Santa Monica, CA, 1955.
20. R. Hassin and A. Tamir, Minimal length curves that are not embeddable in an open planar set: the problem of a lost swimmer with a compass, SIAM J. Control Optim. 30 (1992) 695-703.
21. J. R. Isbell, An optimal search pattern, Naval Res. Logist. Quart. 4 (1957) 357-359.
22. J. P. Jones and J. Schaer, The worm problem, University of Calgary research paper, no. 100, Calgary, Alberta, Canada, 1970.
23. H. Joris, Le chasseur perdu dans la forêt, Elem. Math. 35 (1980) 1-14.
24. R. Klötzler, Universale Rettungskurven, I, Z. Anal. Anwendungen 5 (1986) 27-38.
25. R. Klötzler and S. Pickenhain, Universale Rettungskurven, II, Z. Anal. Anwendungen 6 (1987) 363-369.
26. A. López-Ortiz, On Line Target Searching in Bounded and Unbounded Domains, Technical Report CS-96-25, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 1996.
27. -, Sailor-in-the-fog generalization, in "Open Problems from CCCG 2002," E. Demaine and J. O'Rourke, eds., Proceedings of the 15th Canadian Conference on Computational Geometry (to appear); see also: arXiv:cs.CG/0212050 v2 21 June 2003.
28. V. V. Makeev, private communication (1999).
29. Z. A. Melzak, Companion to Concrete Mathematics: Mathematical Techniques and Various Applications, Wiley, New York, 1973.
30. L. Moser, Poorly formulated unsolved problems in combinatorial geometry, mimeographed (undated, but about 1966).
31. W. O. J. Moser, Problems, problems, problems, Discrete Appl. Math. 31 (1991) 201-225.
32. R. Norwood, G. Poole, and M. Laidacker, The worm problem of Leo Moser, Discrete Comput. Geom. 7 (1992) 153-162.
33. C. S. Ogilvy, Tomorrow's Math, Oxford University Press, Oxford, 1962.
34. C. H. Papadimitriou and M. Yannakakis, Shortest paths without a map, Theoret. Comput. Sci. 84 (1991) 127-150.
35. G. Poole and J. Gerriets, Minimum covers for arcs of constant length, Bull. Amer. Math. Soc. 79 (1973) 462-463.
36. B. Radunović, Convergence in Hausdorff metric preserves geometric shape, Mat. Vesnik 48 (1996) 25-28.
37. D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom, The USSR Olympiad Problem Book, vol. 2, part 2, Tankönyvkiadó, Budapest, 1973 (Hangarian).
38. J. Schaer, The broadest curve of length 1, Univ. of Calgary research paper, no. 52, Calgary., Alberta, Canada, 1968.
39. J. Schaer and J. E. Wetzel, Boxes for curves of constant length, Israel J. Math. 12 (1972) 257-265.
40. G. Tóth, Bellman's problem, Középiskolai Marematikai Lapok 65 (1982) 53-55.
41. J. E. Wetzel, Fits and covers, Math. Magazine 76 (2003) 349-363.
42. -, Sectorial covers for curves of constant length, Canad. Math. Bull. 16 (1973) 367-375.
43. S. W. Williams, Million buck problems, Math. Intelligencer 24(3) (2002) 17-20.
44. V. A. Zalgaller, Extremal problems concerning the convex hull of a space curve, St. Petersburg Math. J. 8 (1997) 369-379.
45. -, How to get out of the woods? On a problem of Bellman, Matematicheskoe Prosveshchenie 6 (1961) 191-195 (Russian).
46. -, Shortest inspection lines for a sphere, unpublished manuscript, St. Petersburg, 1992 (Russian).
47. -, The problem of the shortest space curve of unit width, Mat. Fiz. Anal. Geom. 1 (1994) 454-461 (Russian).