I mean that you keep adding particles as long as they all lie in some semicircle. When the next particle cannot be fit with the others into a semicircle, stop and do not add that particle. The average number of particles I get is 4. -- Gene
________________________________ From: Cris Moore <moore@santafe.edu> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, September 17, 2013 4:49 PM Subject: Re: [math-fun] Probability that all molecules of a gas are in one half of the container
Do you mean 4 is the average number just before I get the origin in the convex hull, or the number when it first is? (I suppose this might be giving away the answer ;-)
On Sep 17, 2013, at 3:19 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:
I get 4.
-- Gene
________________________________ From: Cris Moore <moore@santafe.edu> To: math-fun <math-fun@mailman.xmission.com> Cc: Eugene Salamin <gene_salamin@yahoo.com> Sent: Tuesday, September 17, 2013 1:39 PM Subject: Re: [math-fun] Probability that all molecules of a gas are in one half of the container
Here is a cute question: I place points uniformly in the unit disk (or equivalently on the unit circle). I stop as soon as these points are not all contained in one sector of width pi, or equivalently, as soon as their convex hull contains the origin. What is the average number of points when this first occurs?
Hint: the answer is an integer :-)
Cris
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