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optimize area with a given length

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leo nidas
leo nidas on 12 Feb 2018
Edited: Walter Roberson on 12 Feb 2018
I cannot seem to think or find a theoretical solution to this problem that is described in detail in the link given below. Is there a way of getting an approximate solution by numerically minimizing the objective area? I am not sure how to impose convexity so that I can minimize the objective area. Or even have a more rough idea by forcing the rope to gradually have 2, 3, 4, 5... corners and see what shapes do I get. Any hints help are highly appreciated. Thanks!

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