Not quite. Put a bunch of atoms at Lat 89 deg N, Long 0 deg. Put one atom atLat 89 deg S, Long 0 deg. These all fit within the hemisphere bisected by the Greenwich Meridian. But W is near 89N so its dot product with that last atom is negative. -- Gene
________________________________ From: "rcs@xmission.com" <rcs@xmission.com> To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Sent: Wednesday, September 18, 2013 5:04 PM Subject: Re: [math-fun] Probability that all molecules of a gas are in one half of the container
Wrt part 2 of the puzzle, to provide a test, the following might work: If Vi are the locations of the atoms, compute W = sum Vi. Then see if all the dot products W.Vi are positive.
Rich
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