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which does not have this property, and has a solution consisting of a zig-zag line with three segments of equal length. The solution for many other shapes remains unknown. A general solution would be in the form of a geometric algorithm which takes the shape of the forest as input and returns the optimal escape path as the output.
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A proven solution is only known for a few shapes or classes of shape, such as regular polygons and a circle. In particular, all shapes which can enclose a 60° rhombus with longer diagonal equal to the diameter have a solution of a straight line. The equilateral triangle is the only regular polygon
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It is usually assumed that the hiker does not know the starting point or direction he is facing. The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest. Other variations of the problem have been studied.
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Although real world applications are not apparent, the problem falls into a class of geometric optimization problems including search strategies that are of practical importance. A bigger motivation for study has been the connection to
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as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics.
48:"A hiker is lost in a forest whose shape and dimensions are precisely known to him. What is the best path for him to follow to escape from the forest?"
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What is the optimal path to take when lost in a forest?
187:National Association of Mathematicians Newsletter
98:Bulletin of the American Mathematical Society
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46:. The problem is often stated as follows:
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38:is an unsolved minimization problem in
30:(more unsolved problems in mathematics)
206:"Exploring the Bellman Forest Problem"
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126:Finch, S. R.; Wetzel, J. E. (2004).
36:Bellman's lost-in-a-forest problem
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112:10.1090/S0002-9904-1956-10021-9
21:Unsolved problem in mathematics
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244:Unsolved problems in geometry
136:American Mathematical Monthly
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16:Unsolved geometric problem
249:Recreational mathematics
178:Williams, S. W. (2000).
180:"Million buck problems"
204:Ward, John W. (2008).
93:"Minimization problem"
95:. Research problems.
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128:"Lost in a forest"
44:Richard E. Bellman
239:Discrete geometry
61:Scott W. Williams
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