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The elusive chord


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21 replies to this topic

#1 bonanova

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Posted 15 November 2012 - 11:53 AM

What is the length of a random chord drawn through a unit circle? There are at least four answers.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 Prof. Templeton

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Posted 15 November 2012 - 03:47 PM

Should we randomly chose the definition of random? ;) I know our friend laid out three ways to draw a random chord while leaving out, arguably, the most intuitive way. I thought I remember reading that there were more ways than that even. Math is just a hobby for me so I am not immersed in it.
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#3 brifri238

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Posted 15 November 2012 - 04:01 PM

I am thinking the average length of a random chord is pi/4 (0.7854) as a first thought.
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#4 curr3nt

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Posted 15 November 2012 - 04:18 PM

Spoiler for I'm getting an average of...

Edited by curr3nt, 15 November 2012 - 04:25 PM.

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#5 curr3nt

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Posted 15 November 2012 - 04:47 PM

Spoiler for interesting...

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#6 Prof. Templeton

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Posted 15 November 2012 - 07:18 PM

Spoiler for interesting...


He left out from his three what I thought was the most intuitive way to make a chord

Spoiler for Namely

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#7 CaptainEd

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Posted 15 November 2012 - 07:55 PM

He left out from his three what I thought was the most intuitive way to make a chord

Spoiler for Namely

Spoiler for Professor, I'm uncomfortable with the weight

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#8 Prof. Templeton

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Posted 15 November 2012 - 08:30 PM

Spoiler for Professor, I'm uncomfortable with the weight


I was just pointing out that Bertrand left out that method for choosing a chord. However,

Spoiler for There are more ways to skin a cat

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#9 CaptainEd

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Posted 15 November 2012 - 08:55 PM

Indeed, more than one way.

Bonanova, what is the goal of this puzzle?
a) show us that the notion of "randomly chosen" depends on how you define it?
b) have us show lots of ingenuity in defining truly different ways to define it?
c) elicit from us the really-really-best way to define it?
d) all of the above
e) none of the above
f) other
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#10 Caliban27

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Posted 16 November 2012 - 07:20 AM

I was just pointing out that Bertrand left out that method for choosing a chord. However,

Spoiler for There are more ways to skin a cat

I agree with CaptainEd. Jaynes' solution to the Bertrand paradox shows that random radius (method 2) is the only robust theoretical means of choosing random chord.
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