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November 4th, 2010, 04:44 AM   #1
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A conjecture you might be very interested!

Assume Q is a convex central symmetric curve, whose area is S.
The area of the maximum parallelogram inside Q is S'.

How to prove that S'/S >= 2/pi?

For example, If Q is an ellipse, S'=2ab, S=pi*ab.
If Q is a regular hexagon, S'/S=2/3.
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