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Problem of the Week 1043
Queen Dido's Ghost
Find a function f (continuously differentiable) such that:
Extra Credit: Do this with the value of the integral set to A instead of 1.
Note: While a proof of optimality is not called for, comments are welcome. It might be that there is no function that achieves a minimum length, just a shape that one can approach arbitrarily closely to. Of course, it is allowed to use piecewise functions. Those of you using Mathematica should know that there is a new
Source: The calculus text by Stewart has as a project the investigation of this problem with area 1. Of course, the problem title is a reference to Queen Dido, who wanted to lay out a string of length L against the (straight) coastline of the Mediterranean Sea so as to capture the largest area. The correct answer in that case is to place the string in the shape of a semicircle.
© Copyright 2005 Stan Wagon. Reproduced with permission.