1. ## Numbers

Can anyone tell me how i can dump a cup of marbles on a table and find the location of the cup just by looking at the marbles. They did something on the show Numb3rs about this when charlie found the home of a serial killer by analyzing the places he attacked.

2. Originally Posted by baconbits423
Can anyone tell me how i can dump a cup of marbles on a table and find the location of the cup just by looking at the marbles. They did something on the show Numb3rs about this when charlie found the home of a serial killer by analyzing the places he attacked.
Probably the idea is that if you take the average of the position coordinates of the marbles you should wind up with the position they were dumped at. I would take this supposition with a VERY large grain of salt for a real world problem, though. (The marbles aren't perfectly identical, there are probably objects in the way, different surfaces like a rug or ceramic tile are encountered, the marbles bounce, etc.)

-Dan

3. Can you explain that a little more please

4. It is a TV show they can claim to do whatever they want.

5. See this link if you want to read about the math on NUMB3RS.

Redhawke - All the Math

6. Originally Posted by baconbits423
Can you explain that a little more please
Given the four points (positions) in 2D space:
(1,3)
(-3,4)
(2, -1)
(-1, 2)

The average x value is $\frac{1}{4}(1 - 3 + 2 - 1) = -\frac{1}{4}$

The average y value is $\frac{1}{4}(3 + 4 - 1 + 2) = 2$

So the center of these points is at (-1/4, 2).

-Dan

7. Ok now say i have 4 marbles in a pile in a table and i pick them up ant put them in 4 different spots on the table how can i find the spot of the original pile?

is this even possible

8. Originally Posted by baconbits423
Ok now say i have 4 marbles in a pile in a table and i pick them up ant put them in 4 different spots on the table how can i find the spot of the original pile?

is this even possible
Well, I chose those points randomly to give the example. Presumably if they are spilled onto the table they will all travel to approximately the same distance away from the center so the method would work.

-Dan

9. Look at this picture:

The marbles will distribute something like this. Most in the center and little far away from the center.

If you have an infinit number of marbles that you drop, you drop them exactly straight down, and it is equal chanse they will go in any direction, and there is no obstacles in the way or the surface is different, etc. then you will be able to calculate an exact position for the cup by looking at the position of the marbles and calculating the average position for them. I would say you could even try to calculate from what height the marbles was droped. The longer they have gotten from the average position, the higher up the cup was, a little bit simplified.

But now you don't have an infinite number of marbles, so you can only calculate an approximate value. The more marbles you have the better result you will get. And some other things that you can't ever escape, no matter how many marbles you have, is obstacles in the environment, like table legs, carpets, walls, etc. The cup may have to one one side. Things like that. but besides that, yes, it is possible.

10. Originally Posted by baconbits423
Can anyone tell me how i can dump a cup of marbles on a table and find the location of the cup just by looking at the marbles. They did something on the show Numb3rs about this when charlie found the home of a serial killer by analyzing the places he attacked.
This is a pastiche of a technique used by law enforcement when faced with
a series of similar crimes, which may be presumed to have been committed
by the same perp.

You plot the significant locations on a map, and look at the relationships
between the significant locations and the road network. Criminals often
being lazy and/or stupid can have their area/s of residence and or work
narrowed down by the ease of access to the significant locations from
those places.

The simple centre of mass of the crime locations on its own does not work
well in the real world because geographical space in neither isotropic nor
homogeneous.

RonL

(By-the-by disclosing such information on TV/film police drama makes the job
of catching the perps more difficult, as it draws their attention to how law
enforcement may go about catching them)