Interesting.. i gave it a go and got some results. I’ve divided the the cases into two i) Distance ‘d’ is 1 or larger than 1 and ii) Distance ‘d’ is less than 1. i) The probability will be 2/d*pi. So for example if ‘d’ is 3 probability is 2/3pi. ii) Probability for d will be integral 0 to d ( (cos^-1(x))/pi + 1 - (cos^-1(x-d))/pi ) dx. If ‘d’ is 0.5 probability is 0.41862421 I’d like to make this into another video but I’m not in a situation were i can make one... Not completely sure this is the answer so if you find anything wrong I’d like to hear about it!
Thanks for commenting! The point where the needle first drops will be between 2 line and It could be closer to the top line or it could be closer to the bottom one. But while calculating the probability it doesn’t matter which one it’s closer to. We only need the distance(line ‘x’) from point ‘p’ to the closer line. The distance is limited between 0 to 1 because the distance any point ‘p’ can have to the closest line is limited in 0 to 1.
nicely explained, good luck to you ahead!!
Glad you thought it was nice Thanks:)
@@lemony5823 I would like to know how it affects the result when the spacing is a different number other than 2
Interesting.. i gave it a go and got some results. I’ve divided the the cases into two i) Distance ‘d’ is 1 or larger than 1 and ii) Distance ‘d’ is less than 1.
i) The probability will be 2/d*pi. So for example if ‘d’ is 3 probability is 2/3pi.
ii) Probability for d will be
integral 0 to d ( (cos^-1(x))/pi + 1 - (cos^-1(x-d))/pi ) dx. If ‘d’ is 0.5 probability is 0.41862421
I’d like to make this into another video but I’m not in a situation were i can make one...
Not completely sure this is the answer so if you find anything wrong I’d like to hear about it!
bro, you the best, wish you sucess
I'm a little confused by the line "x". And why you specifically limited it's bounds between 0 to 1.
Thanks for commenting! The point where the needle first drops will be between 2 line and It could be closer to the top line or it could be closer to the bottom one. But while calculating the probability it doesn’t matter which one it’s closer to. We only need the distance(line ‘x’) from point ‘p’ to the closer line. The distance is limited between 0 to 1 because the distance any point ‘p’ can have to the closest line is limited in 0 to 1.
Hello bro can you have simulation code for it to share with us
I’ll try! But might take awhile
tnx bro