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In 1956, the journal of the American Mathematical Society published a short article entitled "Lost at sea" which proposed 3 problems by the famous mathematician Bellman R. The first problem proposed by Bellman R. was the theory to determine the pattern of the curve with the shortest length among all the search curves. The problem was solved by. Isbell J.R in 1957, and solved again by Gluss B in 1961 by replacing the straight shore mainland with an island with radius ܵ Khaltar D. expanded and solve these problems in various ways in his works by connecting with nomadic, pastoralists and geological prospecting activities. In this work, we performed a full analysis by considering two models related to the detection of the enemy's front line and firing point, and these models are extensions of the search problems solved by Isbell J.R and Gluss B. To find the optimal solution, we used the concepts of extremal problem theory and plane geometry.
In 1956, the journal of the American Mathematical Society [1] published a short article entitled "Lost at sea" which proposed 3 problems by the famous mathematician Richard E. Bellman. The first problem proposed by Richard E. Bellman was the theory to determine the pattern of the curve with the shortest length among all the search curves. The problem was solved by John R. Isbell in 1957 [2], and solved again by B. Glass in 1961 [3] by replacing the straight shore mainland with an island with radius S. Khaltar D. expanded and solve these problems in various ways in his works by connecting with nomadic, pastoralists and geological prospecting activities. In this work, we performed a full analysis by considering two models related to the detection of the enemy's front line and firing point, and these models are extensions of the search problems solved by John R. Isbell and B. Glass. To find the optimal solution, we used the concepts of extremal problem theory and plane geometry.
