I have a mathematical conjecture. It has to do with physics, but I call it a mathematical conjecture because the cases I which I generalized into a conjecture were done purely mathematically, with no actual physical experimentation.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a perfect rectangular mirror which obeys the law of reflection exactly and which has side lengths x and y which are coprime integers (meaning they have no common factors except 1). Light is emitted from the topleft corner of the rectangle at a 45 degree angle below the horizontal. Obviously, it will hit the mirror at various points. If the light is absorbed when it hits one of the corners of the rectangle, how many points on the rectangle will the light hit before it is absorbed, as a function of x and y? Alternatively, we can formulate the problem in terms of a pool table, assuming the pool ball and the pool holes are both infinitely small, and the pool ball makes elastic collisions with the sides of the table and friction never slows the ball down.

After considering many values of x and y, I've reached the conjecture that the answer is f(x,y)=x+y-1, but I have thus far not been able to rigorously prove or disprove this conjecture.

Any help would be greatly appreciated.

Thank You in Advance.

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# A Mathematical Conjecture

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