Me again Jerry Changed the setup so that the pellets landing outside the big circle were ignored and just kept going until I had 1000 within the circles in a completely random pattern without Trig. Now the ratio in the smaller circle is 25% or ¼ like the area comparison would suggest.
You do understand math much better than I do obviously! Kelly > On 2Sep, 2020, at 10:10 PM, Dev <d...@porta.ca> wrote: > > Hi Jerry > > I just tried that because I’m no math wizard and need to see things. When > shooting a random shotgun blast of 1000 pellets into the centre of a target > square that contained the large circle and small circles, the ratio worked > out to around 0.2 - not 0.25. It seems the corners outside the big circle > receive about 20% of the shots, the inner circle gets another 20% and the > outer circle gets 60%. So I don’t understand your thought about ¼. > > Kelly > >> On 2Sep, 2020, at 9:43 PM, Jerry Jensen via use-livecode >> <use-livecode@lists.runrev.com> wrote: >> >> Additional thought: >> If you just used random x and y, then ignored points outside the larger >> circle, you would see that 1/4 of the points would be in the smaller circle. >> >> No trig or integrals involved. >> .Jerry >> >>> 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 > _______________________________________________ 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
