Chases and escapes: The mathematics of pursuit and evasion

Chases and Escapes: The Mathematics of Pursuit and Evasion

Volumn , Issue , 2012, Pages

  Nahin, Paul J ^a  

^a UNIVERSITY OF NEW HAMPSHIRE   (United States)

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EID: 84884082943     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (66)

1. Aravind, P. K., "A Symmetrical Pursuit Problem on the Sphere and the Hyberbolic Plane," The Mathematical Gazette 78, 1994, pp. 30-36.
2. Archibald, R. C., and Manning, H. P., "Remarks and Historical Notes," American Mathematical Monthly, February 1921, pp. 91-97.
3. Bacon, R. H., "The Pursuit Curve," Journal of Applied Physics, October 1950, pp. 1065-1066.
4. Bailey, H. R., "The Hiding Path," Mathematics Magazine, January 1994, pp. 40-44.
5. Ball, W.W.R., "Curves of Pursuit," American Mathematical Monthly, June-July 1921, pp. 278-279.
6. Barton, J. C., and Eliezer, C. J., "On Pursuit Curves," The Journal of the Australian Mathematical Society. Series B41, Applied Mathematics, 2000, pp. 358-371.
7. Baston, V. J., and Bostock, F. A., "A One-Dimensional Helicopter-Submarine Game," Naval Research Logistics 36, 1989, pp. 479-490.
8. Bateman, H., Differential Equations, Chelsea 1966, pp. 8-10.
9. Behroozi, F., and Gagnon, R., "A Computer-Assisted Study of Pursuit in a Plane," American Mathematical Monthly, October 1975, pp. 804-812.
10. Behroozi, F., and Gagnon, R., "Cyclic Pursuit in a Plane," Journal of Mathematical Physics, November 1979, pp. 2212-2216.
11. Bernhart, A., "Asymptotic Pursuit," Proceedings of the Oklahoma Academy of Science for 1953, pp. 164-165.
12. Bernhart, A., "Curves of Pursuit," Scripta Mathematica, September-December 1954, pp. 125-141.
13. Bernhart, A., "Curves of Pursuit-II," Scripta Mathematica, Memorial Issue 1957, pp. 49-65.
14. Bernhart, A., "Polygons of Pursuit," Scripta Mathematica, 1959a, pp. 23-50.
15. Bernhart, A., "Curves of General Pursuit," Scripta Mathematica, 1959b, pp. 189-206.
16. Bruckstein, A. M., "Why the Ant Trails Look So Straight and Nice," The Mathematical Intelligencer 15, 1993, pp. 59-62.
17. Cady, W. G., "The Circular Tractrix," American Mathematical Monthly, December 1965, pp. 1065-1071.
18. Clapham, J. C., "Playful MIce," Recreational Mathematics Magazine, August 1962, pp. 6-7.
19. Colman, W.J.A., "A Curve of Pursuit," Bulletin of the Institute of Mathematics and Its Applications, March 1991, pp. 45-47.
20. Croft, H. T., "'Lion and Man': A Postscript," Journal of the London Mathematical Society 39, 1964, pp. 385-390.
21. Davis, H., Introduction to Nonlinear Differential and Integral Equations, Dover 1962, pp. 113-127.
22. Dobbie, J. M., "A Two Cell Model of Search for a Moving Target," Operations Research, 1974, pp. 74-92.
23. Eagle, J. N., "The Optimal Search for a Moving Target When the Search Path is Constrained," Operations Research, September-October 1984, pp. 1107-1115.
24. Eliezer, C. J., and Barton, J. C., "Pursuit Curves," Bulletin of the Institute of Mathematics and Its Applications, November/December 1992, pp. 182-184.
25. Finch, S. R., and Wetzel, J. E., "Lost in a Forest," American Mathematical Monthly, October 2004, pp. 645-654.
26. Gluss, B., "The Minimax Path in a Search for a Circle in a Plane," Naval Research Logistics Quarterly, December 1961, pp. 357-360.
27. Guelman, M., "A Qualitative Study of Proportional Navigation," IEEE Transactions on Aerospace and Electronic Systems, July 1971, pp. 637-643.
28. Guha, A., and Biswas, S. K., "On Leonardo da Vinci's Cat and Mouse Problem," Bulletin of the Institute of Mathematics and Its Applications, January/February 1994, pp.12-15.
29. Hackett, F. E., "A Numerical Solution to the Triangular Problem of Pursuit," The Johns Hopkins University Circular, July 1908, pp. 135-137.
30. Handelman, G. H., "Aerodynamic Pursuit Curves for Overhead Attacks," Journal of the Franklin Institute, March 1949, pp. 205-221.
31. Hoenselaers, C., "Chasing Relativistic Rabbits," General Relativity and Gravitation 1995 (no. 4), pp. 351-360.
32. Isbell, J. R., "An Optimal Search Pattern," Naval Research Logistics Quarterly, December 1957, pp. 357-359.
33. Isbell, J. R., "Pursuit Around a Hole," Naval Research Logistics Quarterly, December 1967, pp. 569-571.
34. Klamkin, M. S., and Newman, D. J., "Cyclic Pursuit or 'The Three Bugs Problem'," American Mathematical Monthly, June-July 1971, pp. 631-639.
35. Koopman, B. O., "The Theory of Search: Kinematic Bases," Operations Research, June 1956a, pp. 324-346.
36. Koopman, B. O., "The Theory of Search: Target Detection," Operations Research, June 1956b, pp. 503-531.
37. Koopman, B. O., "The Theory of Search: The Optimum Distribution of Seaching Effort,' Operations Research, October 1957, pp. 613-626.
38. Lotka, A. J., "Families of Curves of Pursuit and Their Isochrones," American Mathematical Monthly, October 1928, pp. 421-424.
39. Luther, H. A., "Solution to Problem 3942," American Mathematical Monthly, August-September 1941, pp. 484-485.
40. Macmillan, R. H., "Curves of Pursuit," The Mathematical Gazette, February 1956, pp. 1-4.
41. Mangel, M., "Search for a Randomly Moving Object," SIAM Journal on Applied Mathematics, April 1981, pp. 327-338.
42. Morley, F., "The Curve of Ambience," American Journal of Mathematics, July 1924, pp. 193-200.
43. Morley, F. V., "A Curve of Pursuit," American Mathematical Monthly, February 1921, pp. 54-61.
44. Murtaugh, S. A., and Criel, H. E., "Fundamentals of Proportional Navigation," IEEE Spectrum, December 1966, pp. 75-85.
45. Musès, C., "De Morgan's Ramanujan: An Incident in Recovering Our Endangered Cultural Memory of Mathematics," The Mathematical Intelligencer, 1998 (no. 3), pp. 47-51.
46. Perl, T., "The Ladies' Diary or Woman's Almanack, 1704-1841," Historia Mathematica, 1979 (no. 6), pp. 36-53.
47. Puckette, C. C., "The Curve of Pursuit," The Mathematical Gazette, 1953, pp. 256-260.
48. Raina, D., "Mathematical Foundations of a Cultural Project or Ramchandra's Treatise 'Through the Unsentimentalized Light of Mathematics'," Historia Mathematica, November 1992, pp. 371-384.
49. Rees, M., "The Mathematical Sciences and World War II," American Mathematical Monthly, October 1980, pp. 607-621.
50. Richardson, T. J., "Non-mutual Captures in Cyclic Pursuit," Annals of Mathematics and Artificial Intelligence 31, 2001, pp. 127-146.
51. Ruckle, W. H., "Geometric Games of Search and Ambush," Mathematics Magazine, September 1979, pp. 195-206.
52. Ruckle, W. H., "A Discrete Search Game," in Stochastic Games and Related Topics (T.E.S. Raghavan et al., editors), Kluwer Academic 1991, pp. 29-43.
53. Schiebinger, L., The Mind Has No Sex? Woman in the Origins of Modern Science, Harvard University Press 1989, pp. 41-43.
54. Schuurman,W., and Lodder, J., "The Beauty, the Beast, and the Pond," Mathematics Magazine, March-April 1974, pp. 93-95.
55. Seery, M. J., "Pursuit and Regular N-gons," The College Mathematics Journal, May 1998, pp. 228-229.
56. Shukla, U. S., and Mahapatra, P. R., "The Proportional Navigation Dilemma-Pure or True?" IEEE Transactions on Aerospace and Electronic Systems, March 1990, pp. 382-392.
57. Smith, D. E., "On the Origin of Certain Typical Problems," American Mathematical Monthly, February 1917, pp. 64-71.
58. Stone, L. O., "Search Theory: A Mathematical Theory for Finding Lost Objects," Mathematics Magazine, 1977, pp. 248-256.
59. Thews, K., "What Are the Size and Shape of the Largest Region That Can Be Guarded Against a Faster Invader?" American Mathematical Monthly, August-September 1984, p. 416.
60. Washburn, A. R., "Search-Evasion Game in a Fixed Region," Operations Research, November-December 1980, pp. 1290-1298.
61. Watton, A., and Kydon, D. W., "Analytical Aspects of the N-Bug Problem," American Journal of Physics, February 1969, pp. 220-221.
62. Wilder, C. E., "A Discussion of a Differential Equation," American Mathematical Monthly, January 1931, pp. 17-25.
63. Williams, J. D., The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy, McGraw-Hill 1966.
64. Wilson, D. J., "Isaacs' Princess and Monster Game on the Circle," Journal of Optimization Theory and Applications, 9 1972 (no. 4), pp. 265-288.
65. Yuan, L.C.-L., "Homing and Navigational Courses of Automatic Target-Seeking Devices," Journal of Applied Physics, December 1948, pp. 1122-1128.
66. Zelikin, M. I., "On a Differential Game With Incomplete Information," Soviet Mathematics Doklady 13, 1972, pp. 228-231.