Happy Pi day everyone!!
03-16-2019, 04:23 PM
Post: #19
 ttw Member Posts: 248 Joined: Jun 2014
RE: Happy Pi day everyone!!
Sum of reciprocals of integers (limit of course) from One to Infinity (not starring Deborah Kerr and Frank Sinatra) is Pi^2/6.

Probability that two random (will define below) integers are co-prime is 6/Pi^2.

How to uniformly choose an integer at random.
1. Choose a large (not necessarily specified) integer: X.
2. Choose an integer within 1 to X with probability 1/X (using come criterion).
3. If the density of integers satisfy that criterion has a limit as X goes to infinity, the will choose an integer with the proper density.

Example: Choose even integer within 1-x. Probability is either 1/2 or 2X/(2*X+1) which has a limit 1/2 so we can meaningfully say that half of all integers are even.
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 Messages In This Thread Happy Pi day everyone!! - Namir - 03-14-2019, 12:25 PM RE: Happy Pi day everyone!! - ttw - 03-14-2019, 12:34 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-14-2019, 03:53 PM RE: Happy Pi day everyone!! - Dieter - 03-14-2019, 08:09 PM RE: Happy Pi day everyone!! - Eddie W. Shore - 03-14-2019, 01:30 PM RE: Happy Pi day everyone!! - Gerson W. Barbosa - 03-14-2019, 08:58 PM RE: Happy Pi day everyone!! - Gerson W. Barbosa - 03-17-2019, 01:48 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-14-2019, 10:12 PM RE: Happy Pi day everyone!! - DA74254 - 03-14-2019, 10:34 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-15-2019, 12:45 AM RE: Happy Pi day everyone!! - mpark - 03-15-2019, 05:11 PM RE: Happy Pi day everyone!! - EdS2 - 03-16-2019, 07:50 AM RE: Happy Pi day everyone!! - Carsen - 03-15-2019, 04:31 AM RE: Happy Pi day everyone!! - Valentin Albillo - 03-15-2019, 05:07 AM RE: Happy Pi day everyone!! - Ángel Martin - 03-15-2019, 06:35 AM RE: Happy Pi day everyone!! - Carsen - 03-16-2019, 06:27 AM RE: Happy Pi day everyone!! - Thomas Okken - 03-17-2019, 12:38 AM RE: Happy Pi day everyone!! - Geoff Quickfall - 03-15-2019, 07:09 AM RE: Happy Pi day everyone!! - Csaba Tizedes - 03-15-2019, 08:35 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 03:18 PM RE: Happy Pi day everyone!! - EdS2 - 03-18-2019, 08:07 AM RE: Happy Pi day everyone!! - ttw - 03-16-2019 04:23 PM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 05:11 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-16-2019, 10:43 PM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 06:14 PM RE: Happy Pi day everyone!! - ttw - 03-17-2019, 12:56 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-18-2019, 05:40 PM

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