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
