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Polygon in rectangle

Posted on: February 12th, 2014 by
1

Show that every convex polygon of area 1 is contained in some rectangle of area 2.

- via AMS puzzle corner


One Response to Polygon in rectangle

  1. Kevin Chen had this to say about that:

    It is clear if the polygon is a triangle.

    Let d(X,YZ) denote the distance from point X to line YZ.

    Otherwise, consider the longest segment in the polygon formed by vertices A and B. Then consider the farthest vertices C and D of the polygon to line AB on both sides. Then the rectangle with 2 sides length AB and parallel to AB passing through C and D and the other 2 sides length d(C,AB)+d(D,AB) which passes through A and B works as our rectangle.


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