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What is the solution to Dido's problem?

  1. May 19, 2012 #1
    Given a fixed perimeter, what is the geometric shape (non-self-intersecting closed curve) that would maximize the enclosed area? MathWorld (I'm not allowed to link) and a few other sites insist that the answer is a semi-circle, but simple math with perimeter=100 m would show that a circle would have area 2500/[itex]\pi[/itex][itex]\approx[/itex]795.8 m[itex]^{2}[/itex] whereas a semicircle wold have area [itex]\approx[/itex]594.2 m[itex]^{2}[/itex].

    What am I missing?
  2. jcsd
  3. May 19, 2012 #2
    Dido's problem demands that one side of the enclosure is a straight line of fixed length. A circle would not qualifiy, since it has no straight sides.

    If you allow all closed curves, then the circle would be optimal.
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