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#1 2006-06-10 06:31:46

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Geometric probability

What is the probability a random quadrangle to be inscribed (described) in a circle?


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#2 2006-06-10 14:38:38

George,Y
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Registered: 2006-03-12
Posts: 1,306

Re: Geometric probability

the sum of their facing angles to be 180°?

Any circle?

How do you define "random"?


X'(y-Xβ)=0

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#3 2006-06-10 16:33:14

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Geometric probability

An infinitesimal value.  That is, if you define R^2 as the universal set and a circle of finite size.

What you must have is all four points inside the circle.  Find the probability of any single point to be in the circle.  Then raise that value to the fourth power.

For any "usual" set of numbers (naturals, integers, rationals, reals, irrationals, complex), this question doesn't really have an answer since there is an infinite amount of points.  Same goes for any infinite subset of them.  It only starts to have a value when you have points defined on bounded integers.  Of course, then a circle doesn't make much sense, now does it?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2006-06-13 04:16:40

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Geometric probability

Ricky wrote:

An infinitesimal value.

I THOUGHT THE SAME THING!!!


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#5 2006-06-13 05:54:16

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Geometric probability

Ricky wrote:

An infinitesimal value.

well i dont know what you said, but yeh, the chances of just one point being inside the circle is infintisamely small, since the point can be anywhere in infinate space


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#6 2006-06-13 21:34:48

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Geometric probability

But here's what's happening when we restrict the space:
If we have a square with langth, say 1, and a circle in this square, then the probability a point, at random, to be in the circle is the area of the circle. But the amont of points in and out the circle is infty. Why? When you can define the probability as some measure over the space?


IPBLE:  Increasing Performance By Lowering Expectations.

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