Bellman's lost-in-a-forest problem is an unsolved minimization problem in geometry, originating in 1955 by the American applied mathematician Richard E. Bellman.[1] The problem is often stated as follows: "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?"[2] 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.
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 Moser's worm problem. It was included in a list of 12 problems described by the mathematician Scott W. Williams as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics.[3]
Approachesedit
A proven solution is only known for a few shapes or classes of shape, such as a square and a circle. Others, such as an equilateral triangle, remain unknown.[4] 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.
^Williams, S. W. (2000). "Million buck problems" (PDF). National Association of Mathematicians Newsletter. 31 (2): 1–3.
^Ward, John W. (2008). "Exploring the Bellman Forest Problem" (PDF). Retrieved 2020-12-14.
April 05, 2024
bellman, lost, forest, problem, unsolved, problem, mathematics, what, optimal, path, take, when, lost, forest, more, unsolved, problems, mathematics, bellman, lost, forest, problem, unsolved, minimization, problem, geometry, originating, 1955, american, applie. Unsolved problem in mathematics What is the optimal path to take when lost in a forest more unsolved problems in mathematics Bellman s lost in a forest problem is an unsolved minimization problem in geometry originating in 1955 by the American applied mathematician Richard E Bellman 1 The problem is often stated as follows 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 2 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 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 Moser s worm problem It was included in a list of 12 problems described by the mathematician Scott W Williams as million buck problems because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics 3 Approaches editA proven solution is only known for a few shapes or classes of shape such as a square and a circle Others such as an equilateral triangle remain unknown 4 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 References edit Bellman R 1956 Minimization problem Research problems Bulletin of the American Mathematical Society 62 3 270 doi 10 1090 S0002 9904 1956 10021 9 Finch S R Wetzel J E 2004 Lost in a forest PDF American Mathematical Monthly 11 8 645 654 doi 10 2307 4145038 JSTOR 4145038 MR 2091541 Williams S W 2000 Million buck problems PDF National Association of Mathematicians Newsletter 31 2 1 3 Ward John W 2008 Exploring the Bellman Forest Problem PDF Retrieved 2020 12 14 Retrieved from https en wikipedia org w index php title Bellman 27s lost in a forest problem amp oldid 1211242558, wikipedia, wiki, book, books, library,
