Whew !! <grin> > On Sep 2, 2020, at 9:25 PM, Dev via use-livecode > <use-livecode@lists.runrev.com> wrote: > > 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
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