What Angle and Point Ensure a Small Disc Hits a Quadrangle Board Predictably?

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rajeshmarndi
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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.
 

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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.
 
mfb said:
You can calculate each individual collision, sure. Do that n times for the result.
I mean, can there be a general formula, that can determine the angle where it will hit after n collision.
 
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.
 
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.
 
It is deterministic, not random. It is not even chaotic in the mathematical way, but it certainly shares some properties with chaotic systems.