Applied circle packingĀ 

Circle packing is made harder by the following constraints: 

  • The circles are not all the same size, because summer squash are not even close to being cylindrical.
  • Your grill is too small, because you didn’t read the size when you registered for wedding gifts.
  • The plane on which you are trying to pack circles is hot.


Bill Clinton: “if you don’t vote, it’s half a vote for the other guys” – just heard on CNN at a campaign event.

This is a property of elections that hadn’t occurred to me. The quantity Clinton cares about is C – T, where C is the number of votes for Clinton and T the number of votes for Trump.If this is positive, Clinton wins; if it’s negative, Trump wins.  If you vote for Clinton, that goes up by 1; if for nobody, it doesn’t change; if for Trump, down by 1.  So not voting is makes this margin one less than Clinton would like; voting for Trump makes this margin two less.  Hence, half a vote for the other guys.

(My vote can be inferred from my choice of sign convention in this post.)