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Poincaré Conjecture Proven
Posted by Eric on 15 April 2003, 21:52 GMT

We interrupt your regularly-scheduled programming to deliver the news that the Poincaré conjecture has reportedly been solved (though it still must go through a 2-year verification period). For those not familiar with it, the conjecture is one of the seven most important unsolved mathematics problems chosen by the Clay Institute with a $1 million prize each. Check out a dumbed-down explanation of Poincare's Conjecture.

 


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Re: Poincaré Conjecture Proven
Drantin  Account Info

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

     15 April 2003, 23:16 GMT

hehe
RCTParRoThEaD_ Account Info
(Web Page)

heh, was the pun intended?

     15 April 2003, 23:40 GMT

Re: hehe
DarkSlasher117
(Web Page)

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

     16 April 2003, 00:22 GMT


Re: Re: hehe
no_one_2000_  Account Info
(Web Page)

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

     16 April 2003, 02:12 GMT


Re: hehe
Eric Sun  Account Info

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

     16 April 2003, 04:20 GMT

Re: Poincaré Conjecture Proven
no_one_2000_  Account Info
(Web Page)

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*

     16 April 2003, 00:11 GMT


Re: Re: Poincaré Conjecture Proven
jeff m  Account Info

> 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.

     16 April 2003, 01:13 GMT


Re: Re: Re: Poincaré Conjecture Proven
no_one_2000_  Account Info
(Web Page)

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

     16 April 2003, 02:16 GMT


Re: Re: Re: Re: Poincaré Conjecture Proven
yahoolian

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.

     16 April 2003, 03:55 GMT


Mmm.. Donuts.
Tavis Segura  Account Info

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.

     21 April 2003, 19:30 GMT

Re: Poincaré Conjecture Proven
chemoautotroph Account Info
(Web Page)

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

     16 April 2003, 21:55 GMT


Re: Re: Poincaré Conjecture Proven
W Hibdon  Account Info

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-

     16 April 2003, 22:08 GMT


Re: Re: Re: Poincaré Conjecture Proven
Andrew Andrwe  Account Info
(Web Page)

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!

     20 April 2003, 06:04 GMT

Re: Poincaré Conjecture Proven
Dan Rogers  Account Info
(Web Page)

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

     18 April 2003, 00:24 GMT


Fermat's Last Theorem
Jason Chu  Account Info

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

     22 April 2003, 06:10 GMT


Re: Fermat's Last Theorem
Jason Chu  Account Info

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

     22 April 2003, 06:34 GMT

Re: Re: Fermat's Last Theorem
Tavis Segura  Account Info

What about x=y=z=0?

     23 April 2003, 01:07 GMT


Re: Re: Re: Fermat's Last Theorem
CALCUL8R-FREAK  Account Info

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

     2 August 2004, 16:54 GMT


Re: Re: Fermat's Last Theorem
Tavis Segura  Account Info

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

     23 April 2003, 01:21 GMT

Re: Poincaré Conjecture Proven
Bill_pike

Great, now I have to learn topology.

     18 April 2003, 17:12 GMT

Re: Poincaré Conjecture Proven
Geek_Productions Account Info

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

     25 April 2003, 20:49 GMT

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