/sci/ - Science & Math » Thread #10965923

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Anonymous Thu 12 Sep 02:20:12 2019 No.10965923 View Reply Original Report

Quoted By: >>10965931 >>10965933 >>10965946 >>10965954 >>10966008 >>10966021 >>10966153 >>10967561 >>10968994 >>10969107 >>10969295 >>10970607 >>10970615 >>10972535

>Suppose there is a three-dimensional sphere with 4 random points on the surface area. If these 4 points were to be connected to make a tetrahedron as its vertices, what is the probability that the center of the sphere would be encapsulated by the tetrahedron?

How does one solve this?

Anonymous

Anonymous Thu 12 Sep 2019 02:21:40 No.10965931 Report

Quoted By: >>10965938 >>10968215 >>10969377 >>10973143

>>10965923
50 50 it either happens or it doesn't

Anonymous

Anonymous Thu 12 Sep 2019 02:22:15 No.10965933 Report

Quoted By: >>10965938

>>10965923
>what is the probability that the center of the sphere would be encapsulated by the tetrahedron?
50%. It either is inside the tetrahedron or isn't

Anonymous

Anonymous Thu 12 Sep 2019 02:24:09 No.10965938 Report

Quoted By: >>10965940

>>10965931
>>10965933
>Event = probability
Brainlets

Anonymous

Anonymous Thu 12 Sep 2019 02:25:30 No.10965940 Report

Quoted By: >>10965944 >>10974421

>>10965938
>Probability exists
Events either happen or they don't, dummy

Anonymous

Anonymous Thu 12 Sep 2019 02:27:47 No.10965944 Report

Quoted By:

>>10965940
>Not assigning probability based on uncertainty
>Not re-allocating probability when new information is found

frequentist brainlets

Anonymous

Anonymous Thu 12 Sep 2019 02:28:05 No.10965946 Report

Quoted By:

>>10965923
Waste years upon years studying pure mathematics.

Anonymous

Anonymous Thu 12 Sep 2019 02:29:53 No.10965954 Report

Quoted By: >>10965960

>>10965923
probability is 0% because it's so infinitely small that it is 0

Anonymous

Anonymous Thu 12 Sep 2019 02:32:22 No.10965960 Report

Quoted By: >>10967539

>>10965954
probability is infinitely close to 0% that the 4 points will make a plane.

Anonymous

Anonymous Thu 12 Sep 2019 02:46:30 No.10966008 Report

Quoted By: >>10967573 >>10968924 >>10970573 >>10973263

>>10965923
https://www.youtube.com/watch?v=OkmNXy7er84

Anonymous

Anonymous Thu 12 Sep 2019 02:51:40 No.10966021 Report

Quoted By: >>10966091 >>10966104

>>10965923
I'd say do it numerically, but i then I don't think even writing the code would be very easy.

Anonymous

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Anonymous Thu 12 Sep 2019 03:19:54 No.10966091 Report

Quoted By: >>10966104 >>10973156

>>10966021
This would probably suffer from some very tricky mathematical shit. See

https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)

Anonymous

Anonymous Thu 12 Sep 2019 03:22:58 No.10966104 Report

Quoted By: >>10967529

>>10966021
>>10966091
You can generate random points on a 3D sphere with hypercube rejection. Then it's just some tests to see if the center is in. You could define the four planes of the tetrahedron and check which side of each one the center is on.

Anonymous

Anonymous Thu 12 Sep 2019 03:41:44 No.10966153 Report

Quoted By:

>>10965923
https://en.wikipedia.org/wiki/Monte_Carlo_method

Anonymous

Anonymous Thu 12 Sep 2019 18:12:52 No.10967529 Report

Quoted By:

>>10966104
>Then it's just some tests to see if the center is in. You could define the four planes of the tetrahedron and check which side of each one the center is on.
Ya that's the hard part. Maybe not for some people though.

Anonymous

Anonymous Thu 12 Sep 2019 18:15:45 No.10967539 Report

Quoted By:

>>10965960
Since the conditions stated in OP's post rule out situations where a plane is formed, and define the range of possibilities to be considered as those where a tetrahedron is formed, those rare case do not matter anyway.

Anonymous

Anonymous Thu 12 Sep 2019 18:22:51 No.10967561 Report

Quoted By:

>>10965923
Maybe this series of blog posts is relevant

https://johncarlosbaez.wordpress.com/2018/07/10/random-points-on-a-sphere-part-1/

Anonymous

Anonymous Thu 12 Sep 2019 18:27:44 No.10967573 Report

Quoted By:

>>10966008
Amaizing video , too bad no one opens youtube links on 4chan

Anonymous

Anonymous Thu 12 Sep 2019 23:11:53 No.10968215 Report

Quoted By:

>>10965931
Based. This is why homeless people buy lotto tickets

Anonymous

Anonymous Fri 13 Sep 2019 06:23:38 No.10968924 Report

Quoted By:

>>10966008
So I set up an integral before watching this and now I feel dumb.
It was a quintegral.

I did learn a hack that allows me to compute the jacobian without thinking/memorizing so not all is lost.

Anonymous

Anonymous Fri 13 Sep 2019 07:15:32 No.10968994 Report

Quoted By: >>10969017

>>10965923
>>10965923
https://www.youtube.com/watch?v=OkmNXy7er84
here you go

Anonymous

Anonymous Fri 13 Sep 2019 08:00:51 No.10969017 Report

Quoted By:

>>10968994
this is embarrassing for you.

Anonymous

Anonymous Fri 13 Sep 2019 09:57:56 No.10969107 Report

Quoted By:

>>10965923
>Suppose there is a three-dimensional sphere
>posts a pic of a two-dimensional sphere

the answer depends on what you actually meant. for a 3d sphere it's 0

Anonymous

Anonymous Fri 13 Sep 2019 12:30:21 No.10969295 Report

Quoted By: >>10969391 >>10970563

>>10965923
In order to miss the origin all points must be contained in the same half of the surface of the sphere. The chance of all 4 points being on the same half is (1/2)^3

Anonymous

Anonymous Fri 13 Sep 2019 13:42:06 No.10969377 Report

Quoted By:

>>10965931
Based anon solves statistics

Anonymous

Anonymous Fri 13 Sep 2019 13:56:16 No.10969391 Report

Quoted By:

>>10969295
Nice idea, but I think your calculation is off. The division into halves isn't fixed in advance. A large number of 4 points which are not on the same half according to your division will be for some other division.

Anonymous

Anonymous Fri 13 Sep 2019 21:48:17 No.10970563 Report

Quoted By:

>>10969295
Any 3 points are always on the same half.
The chance that the fourth is on the same half is (Area of the spherical triangle of the first 3)/(area of the sphere)

Anonymous

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Anonymous Fri 13 Sep 2019 21:51:28 No.10970573 Report

Quoted By: >>10973599

>>10966008
I understood this perfectly. Does that mean I'm actually not retarded even though I flunked on the puzzle game?

Anonymous

Anonymous Fri 13 Sep 2019 22:03:42 No.10970607 Report

Quoted By: >>10971778 >>10972528

>>10965923
That condition is fulfilled if the 4 points lie on a great circle. Two randomly chose points can always be connected by a great circle. The probability that a third one lies exactly on it is basically zero. For the probability you'd have to compare the volumes of the great circle and the sphere, so one-dimensional measure vs two-dimensional. So it's zero.

Anonymous

Anonymous Fri 13 Sep 2019 22:05:55 No.10970611 Report

Quoted By:

1/8 we can watch YouTube videos you fucking idiot

Anonymous

Anonymous Fri 13 Sep 2019 22:07:19 No.10970615 Report

Quoted By:

>>10965923
1/4 easy, next

Anonymous

Anonymous Sat 14 Sep 2019 07:43:02 No.10971778 Report

Quoted By:

>>10970607
you missed a point.

Anonymous

Anonymous Sat 14 Sep 2019 17:34:04 No.10972528 Report

Quoted By: >>10973186

>>10970607
Tetrahedron, buddy

Anonymous

Anonymous Sat 14 Sep 2019 17:36:27 No.10972535 Report

Quoted By:

>>10965923
this might help: https://www.youtube.com/watch?v=OkmNXy7er84

Anonymous

Anonymous Sat 14 Sep 2019 21:07:16 No.10973143 Report

Quoted By:

>>10965931
based

Anonymous

Anonymous Sat 14 Sep 2019 21:10:29 No.10973156 Report

Quoted By:

>>10966091
literally just linear algebra and vector analysis, brainlet

Anonymous

Anonymous Sat 14 Sep 2019 21:20:17 No.10973186 Report

Quoted By:

>>10972528
Oh fuck. Was too tired.

Anonymous

Anonymous Sat 14 Sep 2019 21:43:05 No.10973263 Report

Quoted By:

>>10966008
Grant is a blessing. It’s frankly amazing a math video has 5 million views.

Anonymous

Anonymous Sun 15 Sep 2019 00:00:40 No.10973599 Report

Quoted By:

>>10970573
its not hard to understand, i.e, be led through, but to come up with it all on your own is what is hard. I believe though that you will benefit from seeing ways past problems have been solved; strengthens your intuition and problem solving skills

Anonymous

Anonymous Sun 15 Sep 2019 08:04:07 No.10974421 Report

Quoted By:

>>10965940
>I roll a dice.
>Get 2.
>There was a 50% chance of this because it either happened or it didn’t.
Fucking hell anon.

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