Exploring the Deterministic Behavior of a Small Disc Hitting a Quadrangle Board

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In summary, the conversation discusses the possibility of determining the angle and point at which a small disc will hit a quadrangle board after n collisions. It is mentioned that a formula can be used for special cases, but in general, each collision must be calculated individually. The idea of randomness is brought up, but it is clarified that the process is deterministic, though it shares properties with chaotic systems.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #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.
 
  • #6
It is deterministic, not random. It is not even chaotic in the mathematical way, but it certainly shares some properties with chaotic systems.
 

What is a formula?

A formula is a mathematical expression that uses symbols and operations to represent a relationship between variables. It is used to calculate a specific result or to solve a problem.

Why do we use formulas?

Formulas are used to express and solve mathematical and scientific concepts in a concise and organized manner. They allow us to perform calculations and make predictions based on data and variables.

How do you create a formula?

To create a formula, you need to identify the variables involved in the relationship and determine how they are related. Then, you can use mathematical operations and symbols to represent that relationship and create a formula.

Can formulas be changed?

Yes, formulas can be changed or modified to better fit the data or to solve a specific problem. However, the basic structure and relationship between the variables should remain the same.

What are some common formulas used in science?

There are many common formulas used in science, such as the Pythagorean theorem, Ohm's law, and the ideal gas law. These formulas are used to calculate various quantities and solve problems in physics, chemistry, and other scientific fields.

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