Monday, March 8, 2010

Fox 260

An obvious extension...

8 comments:

  1. Let take the symetry of the red line on x axis, and suppose that the total red line is not a parabola. it is a circle. then it becomes more easier to see.
    answer is B

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  2. But if you assume that the red curve is a circle, then you'd be distorting the question. Is that not true?

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  3. no,circle is just an example.suppose that parabola is a special case of circle. than the quadrilateral becames a trapezoid, circle is JUST an example

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  4. Oh, I see. I think what you meant was that:
    if the red curve is symmetric, than max-area-quadrilateral MUST be symmetric as well, which in this case a trapezoid. Could be an isosceles triangle, but not in this case.

    That is general statement -intuitively true- but, it would have been an interesting work if one tries to prove this:
    "IF A CURVE IS SYMMETRIC AROUND AN AXIS, THEN INSCRIBED MAX-AREA POLIGON IS, TOO, SYMMETRIC AORUND THE SAME AXIS".

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  5. yeah , you are good man, thanks

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  6. while shape becomes more symmetric, it reaches max area, because it fills the circle and looks like circle.think about a hexagon, or octagon

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  7. area of circle is upperbound for max area of quadrilateral. Like circle, area of under parabola is upper bound too, so the shape should become similar to parabola

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  8. "IF A CURVE IS SYMMETRIC AROUND AN AXIS, THEN INSCRIBED MAX-AREA POLIGON IS, TOO, SYMMETRIC AROUND THE SAME AXIS".
    This statement is NOT true! A counterexample can easily be produced.

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