I don't find it that difficult?

(The "triangular faces" thing is so that you don't have to worry about keeping the vertices of a quadrilateral face coplanar.)

I believe the smallest polyhedron for which this is possible is a cuboctahedron with each square face cut into two triangles.

By the way, there's a discrete version of this: there exists a convex polyhedron with triangular faces such that, by moving the vertices around space continuously, you can turn it inside out without letting any of the dihedral angles go to zero.

I think it's mainly confusing because we can't do it in real life. I truly believe that if someone invented a stretchy material that could pass through itself, people would be able to evert the sphere after a few minutes of trying, doing it hands-on

Try out one of those buttons on the microwave that you've never used before

(though of course the author has made the preprint versions freely available online for years)

Visual description: A copy of The Rising Sea: Foundations of Algebraic Geometry by Ravi Vakil

According to the website it's not published until tomorrow, so I don't know how I have it already. I hit the button labeled "preorder" and they sent it to me

Maybe I would retitle it to "A naive proof, and why it does not work" or "A naive proof and the reason it does not work"

The details of this argument (for instance, that the integral is always a polynomial in pi with integer coefficients of degree at most n, and that it goes to 0 super-exponentially) are left to the reader

IMAGE DESCRIPTION:
The table shows the value of
Integral_{x=0..pi} [sin(x) x^n (Pi-x)^n / n!] dx
for various values of n. For n=7, the exact value is
-112Pi^6 + 50400Pi^4 - 3991680Pi^2 + 34594560
and the approximate value is
0.102692917728.
For n=14, the approximate value is
0.000002476917.

In fact the set of _all_ functions N->R has cardinality c by the same argument

That's still c, isn't it? It seems to me like you're describing cardinality
c^(aleph0) = (2^aleph0)^aleph0
= 2^(aleph0xaleph0)
= 2^(aleph0) = c

I have not seen this film but these two people are playing eyeball

…Godzullah

Mosura? More like Mo-surah

I hope this isn't insensitive
I just noticed the pun and ran with it

Halalgorithms

Robot Muslims pray towards Mecha