Talk:Poolshark

Two parabolas can be used to scale a parallel bundle of rays. Int-e (talk) 18:59, 1 March 2019 (UTC)

It should be possible to construct a mirror that reflects each rational number offset in a parallel bundle of rays at one of two focal points (implementing an arbitrary boolean test). The idea is that one enumerates the rationals, and for each number, picks an available point and corresponding slope. One then restricts the available points such that the slope is enclosed between two curves (parabolas) and an infinite number of choices remain available for all other points. After assigning a slope/point for every rational number this way, a continuous curve on all reals is defined by completing the set (under limits). Int-e (talk) 19:47, 1 March 2019 (UTC)

PS. By choosing the curves enclosing each slope suitably one can also ensure that the path to the focal point will never be obstructed by the mirror. Int-e (talk) 19:53, 1 March 2019 (UTC)

For this purpose it is important to stay outside the circle that has the two focal points as the endpoints of a diameter (shown in red above). Int-e (talk) 21:05, 1 March 2019 (UTC)

PPS. One can recover the parallel bundles (split according to the test) by placing two copies of the magic mirror symmetrically opposite to the two focal points. Int-e (talk) 20:09, 1 March 2019 (UTC)