Heh.. this was on /. this morning...

heh, was the pun intended?

aha - I got it! "Regularily Scheduled PROGRAMMING". And who knows

I'm glad somebody got it... because I didn't ;-)

heh, not really, but hey, I must just be funny like that...

The question doesn't even make sense... what is the question? I think the rubber band would snap if you pulled it "to a point" *confused*

> The question doesn't even make sense... what is the question?

"question" is a little bit inaccurate. the poincare conjecture was pretty much a topological theory (topology is the study of surfaces), which has now been proven to be true.

and i assume you are referring to a topological rubber band - in topology generally things are infinitely stretchy. for example a coffeecup is the same as a donut topologically - take a donut and push part down to make a "cup", twist the rest for the handle, and resize as necessary... so anyway you can stretch things as much as you want - rubber is just an analogy.

Oh... but I still don't see why it would stretch completely down on an apple, but not on a doughnut.

The most a rubber band would shrink on the surface of a doughnut without any part of the rubber band leaving the surface is to the inside ring.

Ehh.. only in one case. There are three ways a rubber band could collapse on a doughnut shape. At some parts of the doughnut, the rubber band could fall into a point, form a ring around the inside and outside of the doughnut (kind of like it would if it were securing a rolled up poster iand the poster's ends met to form a doughnut), or simply form a ring surrounding the doughnut hole.

Wow! That's super cool! But when I told my friends the good news, they had never even heard of the theorm.

This is the first I've EVER heard of it. I think I will keep these in mind, though, when I choose my college classes.

-W-

I'm pretty sure I get it...

so lets talk about a sphere. A sphere, by definition, is a 3 dimensional object, which means it exists in no more and no less than 3 dimensions. And by definition, a sphere is all points in 3d space a certain distance from a center point. That means that any point on the sphere's surface has an equal distance from the center of the sphere than any other point. (all of this is in 3d space).

I think what this is saying is that if you strectch the sphere enough, and in the right way, you can make it so that it is a hypersphere.

A hypersphere is the same thing as a sphere, but it is 4d, and exists in no more and no less than 4 dimensions. By definition, a hypersphere is all points an equal distance from a center point, but that distance also extends into the 4rth dimension. So if you take a center point, and travel an equal distance into the 4rth dimension, then you have a hypersphere.

So it's basically saying you can stretch a sphere of radius 1 into a hypersphere?

I'm reading up on the 4rth dimension...this shiz is crazy stuff!

Aren't the proofs for these beastly math problems hundreds of pages long?

yah, for example, Fermat's Last Theorem was...oh I think 200 pages or so long??? and it is this:

X^N + Y^N = Z^N

where N is a positive whole integer...check it out

i forgot...there are NO solutions for x, y, and z!!!

What about x=y=z=0?

"where N is a positive whole integer"
Positive means greater than zero.

Actually, I think the theorem was supposed to say that there are no pythagorean triples, integer values that solve the equation x^n + y^n = z^n, for values of n greater than 2. I thought someone wrote a proof of it for n=3, but not for any higher levels.

There are infinitely many Pythagorean triples for n=2.. two of them are 3,4,5 and 5,12,13. When you find a triple, you can multiply them by a constant to produce another triple, since (a*x)^2+(a*y)^2 =a(x^2+y^2) =a(z^2) =(a*z)^2

Great, now I have to learn topology.

Ow. My. Brain. Hurts. Thinking in another dimension is hard.