Let's discuss Mathematics

Sleepy or not, I don't think anyone could understand the nitty-gritty of that page in less than a few days, at the very least. This is one of those instances (like Wiles' proof, say) where I will trust the work of the author and the referees.
 
It seems so. At that moment even your post was difficult to read, so I didn't quite notice, how difficult that wikipage could be. Now on second inspection I noticed the word "forcing", and understood that there's no chance I could understand it without some studies.
 
Mandelbrot has died :(

Tribute thread started in OT

http://forums.civfanatics.com/showthread.php?t=392160

Julia has been dead for years. Menger has been dead for years. Koch has been dead for over a century. Cantor... sorry I mean Henry John Stephen Smith... has been dead for years. Sierpinski is long gone also. Hilbert lives in Cantor's Paradise these days. Peano is dead.

Which fractal do you think hardest to invent or discover? Do you have a fractal which you like best, and if so, which one?
 
I think the Mandelbrot set is my fave since it isn't entirely self similar.

Of the self similar ones my favourites are the Sierpinski Triangle



the Menger Sponge



and the Barnsley Fern



EDIT: You forgot Poincarre too ;)
 
I could see something shaped "like" the Menger Sponge standing (maybe I'm wrong though). I couldn't see anything shaped "like" that pyramid standing (unless, of course, there's something else going on).
 
I don't think so...

Roots



Flower

 
So here is a civ related problem (maybe quite easy, I don't know).

In this post ZzarkLinux described a size 13 tile that covers the plane. Picture:

Spoiler :


I marginally changed that to a 13 tile that has more symmetries and also covers the plane; a picture:

Spoiler :


My 13 tile has 3 symmetries: X-axis mirroring, Y-axis mirroring, and 90-degree rotation.

Problem: exactly describe all n such that there is an n-tile that covers the plane satisifying the same 3 symmetries.
 
That looks antisymmetric with respect to x/y axis mirroring.
 
I was thinking of the symmetry of the tile. So we ignore transformations of the form x+a, y+b.
 
Does Fubini's Theorem extend to functions in the complex n-plane?

Yes or no?
 
What's a complex n-plane?

A vector in n complex numbers?

Presumably yes, because those are measurable sets.
 
All squares and all tilted squares (1, 5, 13, 25, ... = n^2 + (n+1)^2) will do; are these all?
 
S-shaped tetris pieces have the same symmetry group as the picture too I believe.

EDIT: Whoops, no 90degree rotational symmetry.
 
What's a complex n-plane?

A vector in n complex numbers?

Presumably yes, because those are measurable sets.

Yeah, that may have come out wrong. I mean like the complex plane is a complex number in 1 variable, so I thought the complex n-plane would be a complex number in 2 variables.
 
That's the vector space Cn
 
So you're still correct that Fubini's Theorem applies in Cn, right?
 
Not sure ;) Integration and measure spaces aren't my strong point. Atticus should be able to help.
 
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