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TRIPLE BEER RINGS
From Problematical Recreations, No. 7
   A man places his beer glass on the bar
    three times to produce this set of triple
    rings. He does it carefully, so that each
    circle passes through the center of the
    other two.
   The bartender things the area of mutual
    overlap (shaded) is less than one-fourth of
    the area of a circle, but the customer says
    it is more than one-fourth. Who is right?
Triple beer rings
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Triple beer rings

  • 1. TRIPLE BEER RINGS From Problematical Recreations, No. 7
  • 2. A man places his beer glass on the bar three times to produce this set of triple rings. He does it carefully, so that each circle passes through the center of the other two.
  • 3. The bartender things the area of mutual overlap (shaded) is less than one-fourth of the area of a circle, but the customer says it is more than one-fourth. Who is right?