Solve this or get the fuck /out/ of my /sci/. I'm not even

1/2 unit

.7 units

>>8400734
This. Approximately

>>8400724
Approximately 0.52140

>>8400741
>>8400734
i assumed so, how do you calculate this?

There are an infinite amount of points inside the square. So the average distance is just the sum so -1/12

>>8400724
Depends on the size of the point

>>8400748
The shortest distance they can be is 0
The largest distance it can be is sqrt 2

The average is half of this.

>>8400748
Don't be a pleb

>>8400751

>-1/12
>negative odds

w-wut?

>>8400757
This can't be right. So if u cut the square in half into a triangle, the average distance wouldn't change?

>>8400734
>>8400757
>>8400770

Yep, this is absolutely wrong in so many ways.

>>8400768
It's possible when talking about infinite points. It's like when mechanics breaks down at the quantum level

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>>8400731
Only correct answer

>>8400734
>>8400741
>>8400746
>>8400748
>>8400751
>>8400755
>>8400757
>>8400777
retards

lmfao this isnt even a math question its fucking common sense

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>>8400777

>>8400784
If it were a circle and not a square then yes the answer would be 1/2.
You're trolling I hope.

>>8400770
No because there's more of the triangle where there's a chance for it to be greater than average than less than average. >>8400773
Its not wrong unless you create a uniform distribution, which wouldn't make sense to use.

>>8400793
But what if you flip the triangle 360 degrees? Doesn't that cause circular distribution?

>>8400724
[math]\frac{1}{15} \left( 2 + \sqrt{2} + 5 \cdot \mathrm{ArSinh} (1) \right) [/math]

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>>8400724
1/2, because either the distance is 1/2 or it isn't

>>8400816
this
http://mathworld.wolfram.com/SquareLinePicking.html

>>8400826
lmao

>>8400807
No, it would be in the same place it was before you flipped it, so it would look the same.

This being Sci and all I'm surprised no one has just, via integration, taken the average value of the distance function over all point pairs in the unit square

>>8400843
Can't be done.

By the way, the solution to this problem was only discovered in 2005.

>>8400724

Assuming you make multiple generations in order to find the average

a = The sum of all the distances
b = half of the total number of points
c = average distance

The answer is
c = a/b

>>8400724
It doesn't matter because it's random, there is no average of something that is not calculated

>>8400848
Are you purposely being dumb?

>>8400827
That probability distribution is wrong though.

Every thread you look at online parrots this solution but there's no justification why.

The truth is, you can't normalize the probability space of this problem.

>>8400848

The integral I wrote certainly wasn't pretty, but it can be approximated well, I suspect.

>>8400854
http://mathworld.wolfram.com/HypercubeLinePicking.html

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>>8400853
reelie mayecks eyiou thinkkkk

>>8400858
Ironic shitposting is still shitposting, and it doesn't make my statement less true

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>>8400724
>mathfags getting this flustered over such a simple problem

Fucking kek. It's not that hard, guys. The answer is 0.765294.

>>8400857
You dumb monkey, 0.52... is the same result you get from integrating four times with respect to x1,x2,y1 and y2. I even ran it in c++ with 100 iterations on each integral to be sure.

What would be the answer if instead of a square it's just a line?

>>8400863
You're absolutely correct, it doesn't make your false statement any more false.

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>>8400867
>I even ran it in c++ with 100 iterations on each integral to be sure.

>>8400912
Nice rebuttal, freshman. Talk to me once you grow the fuck up

>>8400905
1/3

>>8400916
>that delusional overconfidence
I cringed...

https://en.wikipedia.org/wiki/Expected_value

https://www.youtube.com/watch?v=i4VqXRRXi68

>>8400926
Not op, but you can't use this argument by assigning a probability to each pair of points, because there are uncountably many pairs of points to assign a value to.

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>>8400926
You're acting smug as fuck, thinking you're smart just because you memorized a couple of concepts, yet you don't realize how badly you fell for it. I pity you, you're apparently so insecure that you feel the need to assert dominance in a weeb imageboard.

What would be the answer if instead of a square it's a cube or tesseract?

>>8400935
Probability density functions are assigned to continuous random variables all the time. It's a simple probability distribution which can be found here

http://mathworld.wolfram.com/SquareLinePicking.html

>>8400955
It's not simple.
The probability function they used in that paper is wrong.

There's just as many point pairs from 0 to 1 as there are from 1 to sqrt 2.

Monte-carlo's giving me about 0.5214.

>>8400966
They're using standard Lebesgue measure. Read a measure theory book.

>>8400724
>>8400784
1 unit on the side of the square means the diagonal is 1.41 units. Thus 0.59 units is the average.

>>8400979
Wrong.

>>8400979
>Thus 0.59 units is the average.

oops, I divided by 3 instead of 2 for some reason, 0.7

>>8400983
Wrong.

>>8400988
i don't think .005 matters

>>8400988
No, it's 0.7. Brainlet.

>>8400777
gotem

>>8400991
>>8400992
Wrong.

Is it 0.564? Turn square into circle and radius = 0.564. Would the radius of a circle be average distance between 2 random dots on circle?
t. brainlet

>>8401009
Wrong.

>>8401010
What is the answer?

>>8400724
[eqn]\frac{1}{15}(2+\sqrt{2}+5\ln(\sqrt{2}+1))[/eqn]

>>8401016
Read the thread.

>>8401010
Is the average distance a 1/3 of a diametre?
Therefore (0.564*2)/3 = 0.376 is the average distance.

>>8401022
Everyone's arguing and claiming each other is wrong.

>>8401024
No, that has nothing to do with solving it.

>>8401025
Use your brain and figure out who is correct. Pay special attention to externally sourced claims.

>>8401028
It looks like the average is 0.52, based on googling.

http://mathworld.wolfram.com/SquareLinePicking.html

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>>8400858

>>8400975
I think you're being trolled lad.

>>8401076
Wrong.

>>8400751
What steps could you have possibly done to get a negative average distance?

>>8401122
>-1/12
it's just a dumb ass meme
https://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/

>>8400734
got this

>>8400784
I really hope you aren't serious. ~0.59 is the correct answer

>>8400751
Clever troll