

Geometry Puzzle: Center of Square in Circle - pratikpoddar
http://pratikpoddarcse.blogspot.in/2012/11/geometry-puzzle-center-of-square-in.html

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Zenst
My thought process looking at this went like this:

if you look at the possibilities you can take one approach of dividing the
square into four quadrants (like a window) and from that you can see that any
point located in a diagnola opposing will make a hit on the circle. So from
that we know that to pick a spot in one of the four quadrants is 1 in 4 and to
pick the disagonal would be another 1 in 4 chance. As the first picks location
is only relevant for the second pick then it is really just working out the
odd's for the sencond being diagonal.

But there's more. It would be possible for two locations on the same level
dependant upon there location to also make a circle that encompased the centre
fo the square. So what about those permutations, well is you divide those
squares again into four and look at it then you start thinking, this could get
into some recuring details and have an urge to push square pegs into round
holes phsyicaly as well as mentaly :).

That all said anything with a circle has to involve PI, even if you end up
eating a entire pie just to work it out. So as the square has four sides I'm
going to say the answear is 4 multiplied by PI and accept I'm probably wrong
but it is what we call a educated guess.

Though you can imagine after being asked that and finding the right answear to
only be asked; "Now using 3d points, what are the chances of you forming a
sphere that would encompass the centre of a cube", you just know it. Also
would show how adaptable there solution is.

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eru
> So as the square has four sides I'm going to say the answear is 4 multiplied
> by PI and accept I'm probably wrong but it is what we call a educated guess.

That might be somewhat funny: but we are looking for a probability.

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vecter
Quora has a great discussion on this: [http://www.quora.com/Mathematics/What-
is-the-probability-of-...](http://www.quora.com/Mathematics/What-is-the-
probability-of-choosing-two-points-inside-a-square-such-that-center-of-the-
square-lies-in-the-circle-formed-by-taking-the-points-as-diameter)

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Sembiance
Thanks for the link, but Quora won't let me read it unless I sign in, and I
just don't feel like doing that on my iPad. Requiring a log in to read the
page seems a bit backwards thinking to me.

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Sembiance
Ahh, looks like this link explains why Quora has started sucking:
[http://www.businessinsider.com/the-sudden-mysterious-exit-
of...](http://www.businessinsider.com/the-sudden-mysterious-exit-of-a-quora-
cofounder-has-silicon-valley-baffled-2012-10) Not a surprising story. So many
startups pursue money and exits over building a great product. Pushing out
people who made the product awesome to begin with. Now Quora can be counted
among them. Sad really.

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jpdoctor
The problem is ill-posed: _What is the probability of choosing_ does not
describe the _choosing_ process. For example: It turns out that I always
choose my 2 points so that the center-of-the-square is never inside the
circle, so the probability is exactly 0.

Not the answer that anyone is looking for, but shows the importance of
understanding what is asked. Edit: and learning to specify exactly what you
mean when you ask a question. As the saying goes: If you do not learn to write
what you mean, then you will have trouble meaning what you write.

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CKKim
I completely agree with this and always find it instructive to examine wording
thoroughly when posing problems or solutions. However, I think you could come
across more likably by offering a better wording yourself in your comment.
I'll have a shot at it:

"Given two random points inside a square, what is the probability that the
center of the square lies in the circle formed by taking the points as
diameter?"

I'm not happy with my opening clause there though, possibly because I omitted
to explicitly state the distribution (that is, uniform - all points are
equally likely). It seems there is a convention to assume uniform when no
other information is given, but I still don't like "random" there. What would
be your wording?

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pratikpoddar
Changed the problem statement. Thanks

