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

[rajeshmarndi]

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.

 

[mfb]

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.

 

[rajeshmarndi]

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.

 

[mfb]

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.

 

[rajeshmarndi]

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.

 

[mfb]

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