You’re absolutely right. I should have been more careful in describing what I did:
In addition to your method, using polar coordinates, which results in a ratio of ⅓, I also did a random selection of 2 points on the circle in cartesian coordinates which produces the ½. Very curious! I am now wondering if I did the math right? I am known for making many more mistakes than not! Roger > On Sep 5, 2020, at 9:34 AM, Thomas von Fintel via use-livecode > <use-livecode@lists.runrev.com> wrote: > > That is strange. Choosing two points „at random“ should give a ratio of 1/3. > > At least if you choose them by generating two random numbers between 0 and > 360 and use this numbers as angles between a fixed line connecting the > centre (e.g. the x-axis) and the line between the centre and the chosen > point. > Something like (without access to any LiveCode) > put Random(360) *pi / 180 into angle1. > put sin (angle1) * radius into p1y > put cos (angle1) * radius into p1x > That’s the method I would choose. > How do you choose the two points? > > Thomas > > > >> Am 05.09.2020 um 17:11 schrieb Roger Guay via use-livecode >> <use-livecode@lists.runrev.com>: >> >> My intent was not to suggest that math is “really’ broken in the Bertrand >> Paradox, but it did make me wonder what is going on. >> Enter LC. I built a simulation of your description where each of two points >> on a circle are randomly chosen. This kind of chord generation is >> consistently producing a ratio of about ½ which, of course, disagrees with 2 >> of the methods in the BP, but is close to one of them. >> I don’t mean to promote controversy here . . . I am just having fun playing >> with this and wondering what is indeed going on??? >> Thanks for playing, Thomas. >> >> Roger >> >>>>> On Sep 5, 2020, at 12:24 AM, Thomas von Fintel via use-livecode >>>>> <use-livecode@lists.runrev.com> wrote: >>> Having had no contact with Bertrand Paradox except reading the Wikipedia >>> entries in English and German, my impression is that this is not a case of >>> broken math but a case of an ill-defined problem. >>> Saying that a chord of a circle is chosen at random seems to imply that all >>> possible chords are chosen with the same probability. My interpretation >>> would be that all points on the circle have the same probability and also >>> every combination of two points have the same probability of being chosen. >>> Not all methods proposed by Bertrand fulfil this requirement. >>> My interpretation may be wrong. But the fact that you need an >>> interpretation shows that a problem like this needs more clarification. >>> Thomas >>>>> Am 05.09.2020 um 04:40 schrieb Roger Guay via use-livecode >>>>> <use-livecode@lists.runrev.com>: >>>> Bertrand Paradox >>> _______________________________________________ >>> use-livecode mailing list >>> use-livecode@lists.runrev.com >>> Please visit this url to subscribe, unsubscribe and manage your >>> subscription preferences: >>> http://lists.runrev.com/mailman/listinfo/use-livecode >> >> _______________________________________________ >> use-livecode mailing list >> use-livecode@lists.runrev.com >> Please visit this url to subscribe, unsubscribe and manage your subscription >> preferences: >> http://lists.runrev.com/mailman/listinfo/use-livecode > _______________________________________________ > use-livecode mailing list > use-livecode@lists.runrev.com > Please visit this url to subscribe, unsubscribe and manage your subscription > preferences: > http://lists.runrev.com/mailman/listinfo/use-livecode _______________________________________________ use-livecode mailing list use-livecode@lists.runrev.com Please visit this url to subscribe, unsubscribe and manage your subscription preferences: http://lists.runrev.com/mailman/listinfo/use-livecode
