As some mentioned it, this is true iff the length and width are coprime. There's a link to some page to explore this :https://twitter.com/panlepan/status/926390275311853568?s=19 …
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I see that there is now a duo mode to compare the bounces on two rectangles. https://phet.colorado.edu/sims/html/proportion-playground/latest/proportion-playground_en.html …pic.twitter.com/4ia0gRPbmm
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It isn't true... depend from the start point
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The integer sides shouldn't have any common divisors for this to be true. If you scale size by 2 the number rebounds will not change, but with your formula it will change.
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Yes. But also the formula is applicable when the sides are rational. So the original statement is both too specific and not specific enough. It really should be stated in terms of the ratio of the lengths, as in...https://twitter.com/wrose31/status/1126486215958642688 …
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I was waiting for this gif

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What if the table is 5x5? Then no rebounds occur. It seems the gcd of the sides plays a role here
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This is the exact same problem as the DVD screensaver: http://lostmathlessons.blogspot.com/2016/03/bouncing-dvd-logo.html …
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