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Can we determine at what angle, a line will reflect, after hitting n

times the sides of a square.

Lets say we draw a line at a certain angle on one side of a square. It

then reflect to the other side of the wall at a certain angle. And it

continues reflecting on the side of the wall of the square n times.

Is there a general formula that can tell at what angle it will make,

after reflecting n times on the side of a square.

There is certainly a formula that can tell, given the angle it make

first with a wall and at what angle it will make on the other side of

the square, after reflecting. But what angle it will make after

reflecting n times, is there any?

Is it right, we have to go calculating for each reflection to get the

angle, after n reflection?

Isn't, this is how a computer find the angle after n reflection?

One thing is for sure, for a certain square, for each angle it make at

a certain point on one side of a square, after n reflection on the

square, it will hit a certain side at a certain point and at a certain

angle.

But I just can't think of a general formula, that can tell at what

point or at what angle it is going to hit on a certain side of the

square.

Thank you.

If the initial angle made with the side of the square is x, and the coefficient of restitution is unity, after an odd number of bounces, the angle will be 90-x, and after an even number of bounces it will be x.

If the coefficient of restitution is e, after an odd number of bounces, n, the angle will be given by

arctan(e^n*cot(x)) and after an even number of bounces arctan(e^n*tan(x)). This means that as time goes on, the ball gets closer to the sides of the square.

Regards

vijilant

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Comment | Thanks a lot, the reply was so soon. I didn't understand coefficient of restitution but I will have a look at it. |

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