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Does this have a formula?

  1. Sep 28, 2014 #1
    If we hit this quadrangle board(see the attachment) with a small disc on one of its wall, at a certain point with a certain angle, it will hit the four wall many times.

    Can we determine at what angle and at what point, the small disc will hit on the wall after n hit on the wall.

    That is, can it have a formula?

    Also when a computer shows the result, does it calculate for each hit on the wall and then reach, where the final hit will be.

    Thanks.
     

    Attached Files:

  2. jcsd
  3. Sep 28, 2014 #2

    mfb

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    You can calculate each individual collision, sure. Do that n times for the result. Due to rounding errors, the prediction will become bad if n is too large.
     
  4. Sep 28, 2014 #3
    I mean, can there be a general formula, that can determine the angle where it will hit after n collision.
     
  5. Sep 29, 2014 #4

    mfb

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    Not in general, as you have to calculate the correct border every time. For special cases (like rectangles, some triangles and so on), yes there is.
     
  6. Oct 6, 2014 #5
    Does this mean, for a specific side a,b,c,d(except special cases you mentioned which are symmetry) the hit on the wall, will be said to be irregular. If irregular, then isn't it become random???

    I know it cannot be said to be random, as the hit depend upon the position where the previous hit was. It is just that, it cannot be determined through a general formula. If I'm right, just like the generation of Prime numbers.
     
  7. Oct 6, 2014 #6

    mfb

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    It is deterministic, not random. It is not even chaotic in the mathematical way, but it certainly shares some properties with chaotic systems.
     
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