Jerry, You’ve done a very nice job of describing what’s actually(?) happening in my code, but I think you missed the point of my question. You agree that if you simply sample random pixels then the ratio of a random pick inside the smaller circle will depend on the area of the circles. And, if I pick a random x and y within the concentric circles of radius R and 2R, ¼ of the time they will lie in the smaller circle and ¾ of the time in the bigger. So, pick any random x and y and convert to radial coordinates. Everything should work! In my code I pick a random angle and a random radius (radial coordinates) within the limits of the larger circle, thus picking random points within the area of the larger circle, yet I get ½ (which you say is the right answer). My intent was to pick random points (using radial coordinates) for which the result should be ¼!
What’s wrong with my code? Thanks, Roger > On Sep 2, 2020, at 8:27 PM, Jerry Jensen via use-livecode > <use-livecode@lists.runrev.com> wrote: > > 1/2 is the right answer. > > Take your drawing of the circles. Cut a verrrryy thin radial slice from the > center to the outside circle. So thin that it is just a line. > > Now think of how likely a random point on that line will be in the part of > the line that was in the smaller circle. The part that was from the smaller > circle is HALF as long as the entire line. > > Now add up all the possible positions of that line. Why would that change the > answer? > > Congratulations, you understand integrals! > .Jerry > >> On Sep 2, 2020, at 7:38 PM, Roger Guay via use-livecode >> <use-livecode@lists.runrev.com> wrote: >> >> Your chance to be Genius du Jour: >> >> If I construct 2 concentric circles, one being half the radius of the >> larger, then simple math shows that the smaller circle has an area ¼ the >> area of the larger. >> Now if I generate a random point within the radius of the larger circle, I >> should expect that the probability of it landing in the smaller circle to be >> ¼. >> But, I must be doing something wrong because I get ½ ! >> >> Here is my script: >> >> on mouseDown >> >> getStuff >> >> end mouseDown >> >> >> local tR, tTheta, tX0, tY0, tX1, tY1, tTotCount, tL, tLongCount >> >> on getStuff >> >> put item 1 of the loc of grc OuterCircle into tx0 >> >> put item 2 of the loc of grc OuterCircle into tY0 >> >> put "" into tTotCount >> >> put "" into tLongCount >> >> emptyFlds >> >> end getStuff >> >> >> on mouseUp >> >> lock screen >> >> repeat 1000 >> >> put random(200) into tR -- 200 is half the width of the larger >> circle >> >> if tR > 1 then >> >> ## put random(2*pi) into tTheta1 >> >> get random(360) >> >> put it*pi/180 into tTheta1 >> >> put tR*cos(tTheta1) into tX1 >> put tR*sin(tTheta1) into tY1 >> >> set the loc of grc Ptgrc to tX0 + tX1, tY0 - tY1 --- >> grc Ptgrc is a 2 pixle oval >> >> if intersect(grc Ptgrc, grc InnerCircle, "opaque >> Pixels") then add 1 to tLongCount >> >> add 1 to tTotCount >> >> end if >> >> end repeat >> put tTotCount into fld "totcountFld" >> >> put tLongCount into fld “LongCountFld" >> >> put tLongCount/tTotCount into fld "RatioFld" >> >> unlock screen >> >> end mouseUp >> >> >> Apparently, this does not generate a random point within the larger circle! >> Can someone please tell me what’s wrong here? >> >> Thanks, >> Roger >> _______________________________________________ >> 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
