Results 1 to 10 of 10

Math Help - Numbers

  1. #1
    Newbie
    Joined
    Jan 2007
    Posts
    3

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,894
    Thanks
    326
    Awards
    1
    Quote Originally Posted by baconbits423 View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2007
    Posts
    3
    Can you explain that a little more please
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    It is a TV show they can claim to do whatever they want.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    See this link if you want to read about the math on NUMB3RS.

    Redhawke - All the Math
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,894
    Thanks
    326
    Awards
    1
    Quote Originally Posted by baconbits423 View Post
    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
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2007
    Posts
    3
    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
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,894
    Thanks
    326
    Awards
    1
    Quote Originally Posted by baconbits423 View Post
    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
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member TriKri's Avatar
    Joined
    Nov 2006
    Posts
    357
    Thanks
    1
    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.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by baconbits423 View Post
    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)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 29th 2011, 02:18 AM
  2. Replies: 1
    Last Post: September 27th 2010, 03:14 PM
  3. Proof: All rational numbers are algebraic numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 5th 2010, 10:26 AM
  4. Replies: 3
    Last Post: April 10th 2008, 05:58 PM
  5. Proving Lucas Numbers and Fibonacci Numbers
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 18th 2008, 11:33 PM

Search Tags


/mathhelpforum @mathhelpforum