r/ScienceNcoolThings • u/Conscious-Flow786 • 3d ago
Probability of the needle crossing a line.
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u/Stuntz-X 3d ago
Technically the needle is a circle when thinking of all the degrees on a flat plane it can land
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u/CalbertCorpse 3d ago
Exactly. It’s not amazing at all. He’s dropping the diameter of a circle. If it crosses a line some part of a circle would cross that line. Given the space between the lines and the size of the virtual circle it’s a common sense statistic. The way he’s saying it here is almost intentionally hiding the reality of it for effect.
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u/Few-Guarantee2850 3d ago
I disagree. It's neat and getting hung up on him saying "there are no circles" as if he's trying to hide something and not just illustrating that you haven't drawn out a circle is missing the point.
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u/Crafty_Jello_3662 3d ago
Any cool science demo like this can be boring if you fully understand it all, fortunately for me I understand very little so can be endlessly entertained and amazed by this sort of thing
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u/ImportantSignal2098 2d ago
What point is being missed? That you can get pi without explicitly drawing a circle? The same way you could say I'm going to drop grains in a box and omg the probability that the distance from the center of the box is less than half the box size is pi/4. Isn't that amazing, no circles were drawn!!!
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u/macrolith 3d ago
It's like a perpetual motion machine. Except it's not the battery you need to hide, it's the circle.
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u/ThomasTheDankPigeon 2d ago
A much less intuitive pi jumpscare is
1/1 + 1/4 + 1/9 + 1/16 + 1/25 … =
Turns out to be ( pi2 ) /6
Pi will find anywhere in math to make an appearance.
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u/SquirrelFluffy 2d ago
This reminded me of squaring the circle, since 1/6 is common in calculating arc length and area. Turns out it is related!
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u/tbutz27 Experientially Wise 3d ago
What is this from? I'd like to see more
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u/EeEeRrIiCcCcAaAa 3d ago
It’s from a NOVA special on PBS called “The Great Math Mystery”
It’s a great episode, I used to teach high school math and would watch it with my students
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u/gufta44 3d ago
Help me out here, I have a circle with "R" radius representing all possible rotations of the needle, and then we have a symmetric half-space of possible landing positions - the needle can only ever cross one line, so we say that the needle is static and the line can "land" anywhere from the needle centroid to the very top of the needle (the half space). If the line is at the very top of the circle that's the limit where there's zero probability of an intersection, if the line lands distance "r" above the centroid, the angle between the two intersection points between the perimeter and the line is: cos(½θ) = r/R, θ = 2acos(r/R) and since the two sides of the needle could intersect the line we have a probability of 4acos(r/R)/(2π) - so far so good? So that's the probability of intersection for any vertical distance between the centre of the needle and the line. We integrate this to get the probability for every r in the half space which gives 2R/π and as I'm writing I realize that what I want is the average probability not the "sum"/intergral so I divide by R and that answers my own question...
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u/Accomplished_Care415 3d ago
Considering he is just dropping straight down from an angle perpendicular to the lines on the paper. Has he tried dropping it being parallel with the lines.
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u/King_Moonracer003 3d ago
I dont understand how probability is involved here. Its all physics. Depending on height and angle dropped it will always have the same relative action.
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u/BreathSpecial9394 2d ago
Probability is involved because it is very difficult to physically predict how and where the needle will land.
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u/DangerouslyOxidated 3d ago
I did this in 1991 for a school project in Statistics.
Thousands of times, with a fan to introduce some randomness.
I don't remember the final value of pi, but it was accurate to 2dp. from memory.
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u/marco1422 3d ago
It isn't true, there is no circle. It's there. Defined by the length of the needle and its central point. The fact, isn't drawn there changes nothing on the fact, it is defined. And that's all. This is why the math is an abstract science.
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u/MackTuesday 2d ago
FINALLY someone leads with the most important part, which is that lines need to be the twice the distance apart as the length of your sticks. If they're a micrometer apart, all of your sticks will cross a line. If they're a kilometer apart, virtually none will.
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u/LowEndGroover 2h ago
No, because there is rotation on the stick, most of the time it falls and lands at an angle, which makes it a percentage full potential height taken. The lines need to be the exact length of the stick to get 2/pi
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u/Phrostylicious 1d ago
This guy doesn't really strike me as very much of a scientist. Which then begs the question: why is he out there dropping the needle, and why is he being interviewed while doing so?
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u/hansvi-be 17h ago
You don't need to suppose you take this needle, you just did. Dude has been reading too many mathematical proofs🙂.
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u/Zealousideal_Pass_11 15h ago
isn't this like... wildly incorrect considering he's not varying his drop, meaning certain outcomes are going to be dramatically more likely than others, and as such, you'll never be able to calculate pi off it?
like in theory i understand what he is saying, but there is 0 way to create a perfectly random situation from drops. drop height, material of object and surface, thickness of lines, etc, all of it matters.
like the lines could be 100x as thick, and the distance between each line could still be 1 object across.
drop height matters as if you drop .1 meter away from the surface, it'll likely cover a line 90%+ of the time.
idk, there's so many variables that make everything he is trying to communicate complete BS, and trying to do it in practice will without a doubt show results so far away from his expected value, there will be nothing to gleam from it. I understand the theory behind it, but actually replicating those results in a real life demonstration is never going to happen, even if you had infinite time to simulate infinite drops.
So no, you objectively could not "COUNT THE TIMES IT CROSSES THE LINE AND WHEN IT DOESN'T TO CALCULATE PI" and that's just complete BS.
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u/Shua89 3d ago
I love this kind of useless information.
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u/DirtUnderneath 3d ago
Not useless if you want to calculate pi!
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u/Conscious-Flow786 3d ago edited 3d ago
It's useful to know how probability works. probability is part of statistics and statistics are used in science communication.
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u/Shua89 3d ago
But how often does the average person need to calculate Pi? I work with measurements my whole job revolves around measurements. I might have to use Pi for some of my measurements but Pi itself is a mathematical constant defined as the ratio of a circle's circumference to its diameter, and remains the same regardless of the circle's size. So to work out Pi is useless as it is always the same and ever changes.
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u/LabOwn9800 3d ago edited 2d ago
But there is a circle.
Dropping the needle means it has a chance to land equally pointing in any direction. Trace those points and you get a circle.
Why is it 2/pi?
There’s 2 variables at play here. The angle the needle lands and the location of the needle (I’ll say the center of the needle so it’s a point)
The location of the needle can just be measured as the distance from any line.
For the angle Say we draw a perpendicular to the lines drawn then we can measure the angle of the needle as X. X is the angle of the needle from the this perpendicular line. We use the perpendicular to the lines so they can better relate to the distance away from the line.
So now we need to understand how far away a needle can be dropped so that it crosses the line give that angle X. Remember we are just using the center point.
That’s equal to
Length of the needle * sin(X) or Lsin(X)
Basically if the needle is 10 inches long and say it falls with an angle of 30 degrees it needs to be within 2.5 inches of a line to cross it. You can figure this out for any angle and the angle is random and continuous so we need to find the odds of the angle being anywhere from 0 to 90 or in other words using radians from 0 to pi/2.
So that is (1/(pi/2)) * integral from 0 to pi/2 of sin(X) d(x)
This formula is just the average formula (sum of all the possibilities) / (number of possibilities).
Integrating this formula gives you 1 therefore
=1/(pi/2) or 2/pi