### Poincare' conjecture

I feel like I should say something meaningful since Grigory Perelman solved the Poincare Conjecture which states that

Without going into homology, I'll try to explain in laymen's terms...Basically any 3-d bounded blob (ex. no feelers going off into infinity) living in 4-d can be collapsed into a sphere without ripping, tearing or ajoining. Yeah, that was a bad attempt. There's a reason why I don't teach anymore! The Clay Mathematics institute is much more eloquent than I.

You're probably going,

This happens to be one of my favorite topological verities.

It's a fractal (a type of Cantor set to be exact), so as you zoom into those horny parts, you see more detail. This blob is homeomorphic to a sphere.

I think its interesting the conjecture has been proven for higher dimensions prior to Perelman's contribution for n=3. Humans are 3 dimensional creatures coexisting with time, in a 4 dimensional space. Perhaps it was because we live too close akin to the objects in question which is why n=3 alluded mathematicians for so long.

**

To the person who said bunnies are the same as spheres....That's not true! The digestive track runs from mouth to anus, so they are tori. Okay, I'm done ranting now.

*any closed simply connected 3-dimensional manifold is homeomorphic to the standard 3-dimensional sphere.*Without going into homology, I'll try to explain in laymen's terms...Basically any 3-d bounded blob (ex. no feelers going off into infinity) living in 4-d can be collapsed into a sphere without ripping, tearing or ajoining. Yeah, that was a bad attempt. There's a reason why I don't teach anymore! The Clay Mathematics institute is much more eloquent than I.

You're probably going,

*oh come on, how complicated can a blobby thing be?*Heh. I present to you the Alexander Horned Sphere:This happens to be one of my favorite topological verities.

It's a fractal (a type of Cantor set to be exact), so as you zoom into those horny parts, you see more detail. This blob is homeomorphic to a sphere.

I think its interesting the conjecture has been proven for higher dimensions prior to Perelman's contribution for n=3. Humans are 3 dimensional creatures coexisting with time, in a 4 dimensional space. Perhaps it was because we live too close akin to the objects in question which is why n=3 alluded mathematicians for so long.

**

To the person who said bunnies are the same as spheres....That's not true! The digestive track runs from mouth to anus, so they are tori. Okay, I'm done ranting now.

## 2 Comments:

Hi, Cindy --

You lost me after " I feel like I should say something meaningful since Grigory Perelman solved the Poincare Conjecture which states that..."

Huh?

Sandy

Hee hee...if you're really dying to know, I can draw pics of this theorem over lunch one day.

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