Post problems in which the answer is simple but the solution is hard.
>How many spheres can touch a center sphere in three dimensions?
12
>hard
What is sphere packing ?
But I guess it is quite hard to prove it mathematically tbf
>>7951533
is what I was talking about, it was meant to be more like a game. I have another one to break the ice:
>What happens if you mix Red and Green?
You get Yellow
:^)
>>7951548
No you get BROWN
>>7951552
With RGB colours you get yellow
regards different poster and anonymous not-OP
>>7951552
yeah should've thought twice before posting, better one would've been
>What color we see the most shades of?
Green
Fermat's last theorem:
>Are there any values a, b, and c such that a^n + b^n = c^n for n > 2? (other than a=0, b=0, c=0)
No.
>>7951620
could you write a 3D plot with a and b as incognites
>>7951620
This seems kind of intuitive. The proof of this is really that crazy?
>>7951748
It's the craziest proof.
>>7951507
What of the center sphere is really big and the outer spheres are really small?
Checkmate Euclid
>>7951507
>How many circles can touch a center circle in two dimensions?
6
>>7951755
There is an obvious size-dependency on nearest neighbors in hard sphere and hard disk packing.
>>7951748
This is most of it, but it relies on some previously proven things you can find in the references.
http://www.math.ias.edu/~anindya/fermat.pdf
>>7951781
proof?
>>7951852
hexagonal packing is the most efficent packing
>>7951748
>This seems kind of intuitive.
Sure. And people have tried fitting the proof into the margin of a text once but it just didn't fit.
>The proof of this is really that crazy?
It usually starts out by people saying "This seems kind of intuitive" and then they go crazy.
What is the limit of
[math] -\frac {1} {1}, -\frac {1} {1+2}, -\frac {1} {1+2+3}, -\frac {1} {1+2+3+4}, \dots [/math]
Answer:
It equals the number of spheres that can touch a center sphere in three dimensions
>>7951755
This. What are the additional constraints on the spheres that OP failed to mention?
>>7952483
>not even bothering to take the reciprocal and multiply by -1
do you just ejaculate memes whenever you see the number 12
>>7952512
>(you)
>>7951507
>does [recently proved hard theorem] not hold
>no
Fun thread.
infinite you just gotta make the spheres really smal
>>7951507
>does pi(x) ~ x/lnx?
>yes
>can we decompose any symmetric matrix[math] A \in \mathbf{S}^n[/math] with the symmetric eigenvalue decomposition (SED)
[math] A = \sum_{i=1}^n \lambda_i u_iu_i^T = U \Lambda U^T, \Lambda = \mathbf{diag}(\lambda_1,l\dots,\lambda_n) [/math]
where the matrix of [math]U := [u_1 , \ldots, u_n][/math] is orthogonal (that is, [math]U^TU=UU^T = I_n)[/math], and contains the eigenvectors of A, while the diagonal matrix [math]\Lambda[/math] contains the eigenvalues of A?
>yup
>>7952489
Spheres of equal diameter.
>>7951620
a=0, b=1, c=1 :^)
>>7951548
Depends on whether you're talking about pigments or light.
>>7953212
OH SHIT WILES WAS WRONG
>>7951748
How is it intuitive?
>>7951507
>How many spheres can touch a center sphere in three dimensions?
infinitely many infinitely tiny spheres on a considerably larger center sphere.
at least you meant well, OP.
Hm. Questions in number theory are cheating. Let me think of problems like OP's outside of number theory. Also, yes/no questions don't follow the spirit of OP.
Ok:
1. Write a program which outputs its own syntax.
Solution: Google "Quine" and you'll find an example.
2. Find a finite set of polygons that tile the plane aperiodically.
Solution: Google "penrose tiling".
>>7951507 this isnt as difficult as you think. maybe you've learned the solution different way than I have but im pretty sure a child could find the closest packing structure of a sphere, given some marbles and a few minutes. there just arent that many configurations
>>7951748
>This seems kind of intuitive. The proof of this is really that crazy?
t. every non-mathematician's opinion since the beginning of time
And I mean that for all mathematical ideas, not just Fermat's Last Theorem.
>>7951781
This is so easy to prove though
>>7952050
>being a meme scientist
nice proof :)
>>7951507
>the answer is simple but the solution is hard.
Question: How to stop being lonely.
Answer: Get a girlfriend.
>>7954399
I am a /sci/entist. B-but what is a girlfriend?
