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# Points on a circle

Best Answer bubbled, 06 May 2014 - 05:47 AM

Spoiler for My take

Go to the full post

16 replies to this topic

### #1 bonanova

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Posted 02 May 2014 - 10:28 AM

What is the probability that n points placed at random on the circumference of a circle all lie on a semicircular arc?

That is, for at least one of the points, all the others lie [0, pi] radians from it.

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### #2 DeGe

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Posted 02 May 2014 - 04:45 PM

Spoiler for Points

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### #3 Rob_G

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Posted 02 May 2014 - 07:13 PM

Spoiler for Points

Spoiler for I have to disagree

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### #4 Rob_G

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Posted 02 May 2014 - 07:53 PM

Spoiler for I wanna say

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### #5 m00li

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Posted 03 May 2014 - 08:17 AM

Spoiler for complex

The 'aha' solution you are looking for might not be applicable for a sphere. am i right?

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### #6 plasmid

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Posted 03 May 2014 - 03:28 PM

m00li: if you start with points 0 and x and then add a third point y that is within a semicircle containing 0 and x but y is not between 0 and x, then the probability of another point being in a semicircle with all three of those is no longer 1-x/2pi but is 1-(longest distance between any of 0 x and y)/2pi

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### #7 m00li

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Posted 04 May 2014 - 06:48 AM

Yes, the solution is absolutely incorrect
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### #8 DeGe

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Posted 04 May 2014 - 09:44 PM

Spoiler for Slight change

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### #9 bonanova

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Posted 05 May 2014 - 12:58 AM

Spoiler for Slight change

What if you picked a different starting point?

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### #10 bubbled

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Posted 06 May 2014 - 05:47 AM   Best Answer

Spoiler for My take

Edited by bubbled, 06 May 2014 - 05:52 AM.

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