Home | Community | Message Board


Kratom Eye
Please support our sponsors.

General Interest >> Science and Technology

Welcome to the Shroomery Message Board! You are experiencing a small sample of what the site has to offer. Please login or register to post messages and view our exclusive members-only content. You'll gain access to additional forums, file attachments, board customizations, encrypted private messages, and much more!

Jump to first unread post. Pages: 1
Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 7 years, 5 months
The Hairy Ball Theorem
    #11194647 - 10/06/09 05:39 PM (8 years, 10 months ago)

I thought some people here would enjoy seeing it.

The theorem states that a continuous vector field tangent to the sphere must contain a zero vector. In less abstract terms, it states that you cannot "comb a hairy ball without creating a cowlick".

A picture is worth a thousand words :



For instace, this is not true of a torus :



This is related to the fact that there is no three-dimensional equivalent of the complex numbers. The 3-sphere (the surface of a four-dimensional ball) does admit continous, nonvanishing tangent vector fields, and this is in turn related to the fact that there is a four-dimensional equivalent of the complex numbers (the quaternions).


--------------------
Formula: 0


Post Extras: Print Post  Remind Me! Notify Moderator
InvisibleChespirito
Stranger
Male User Gallery


Registered: 02/13/09
Posts: 3,259
Re: The Hairy Ball Theorem [Re: isaacein]
    #11194785 - 10/06/09 05:58 PM (8 years, 10 months ago)

Ha I dont know much about topology, however I was at a party once and my friends topology professor was there for some reason.  My friends and I were trashed and we made fun of him and his field for having a theory called the Hairy Ball theorem.  Seemed amusing at the time though we were plowed under man, I think I sexually harassed him afterwards just to see how obnoxious I could be.  Ah undergrad


Post Extras: Print Post  Remind Me! Notify Moderator
Invisiblecortex
[ H ] ψ = [ E ] ψ
Male User Gallery

Registered: 10/08/02
Posts: 15,167
Loc: Gedankenexperiment
Re: The Hairy Ball Theorem [Re: Chespirito]
    #11194815 - 10/06/09 06:03 PM (8 years, 10 months ago)

:lol:


--------------------

Signature (up to 750 characters).


Post Extras: Print Post  Remind Me! Notify Moderator
Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 7 years, 5 months
Re: The Hairy Ball Theorem [Re: Chespirito]
    #11195032 - 10/06/09 06:34 PM (8 years, 10 months ago)

Quote:

Chespirito said:
Ha I dont know much about topology, however I was at a party once and my friends topology professor was there for some reason.  My friends and I were trashed and we made fun of him and his field for having a theory called the Hairy Ball theorem.  Seemed amusing at the time though we were plowed under man, I think I sexually harassed him afterwards just to see how obnoxious I could be.  Ah undergrad




Haha! Good story.


--------------------
Formula: 0


Post Extras: Print Post  Remind Me! Notify Moderator
OfflineChuangTzu
starvingphysicist
Male User Gallery


Folding@home Statistics
Registered: 09/04/02
Posts: 3,060
Last seen: 4 years, 10 months
Re: The Hairy Ball Theorem [Re: Chespirito]
    #11195683 - 10/06/09 08:13 PM (8 years, 10 months ago)

Quote:

Chespirito said:
I think I sexually harassed him afterwards just to see how obnoxious I could be.




Did you tell a lewd version of the coffee cup and donut joke?


Post Extras: Print Post  Remind Me! Notify Moderator
InvisibleAnnapurna1
liberal pussy
Female User Gallery

Registered: 05/21/02
Posts: 5,646
Loc: innsmouth..MA
Re: The Hairy Ball Theorem [Re: isaacein]
    #11197978 - 10/07/09 01:54 AM (8 years, 10 months ago)

heres a couple of proofs...but dont ask me to try to make head or tail out of them ..

http://www.math.byu.edu/~jarvis/sperner.pdf
http://topologicalmusings.wordpress.com/2008/07/22/analyzing-the-hairy-ball-theorem/


--------------------


"anchor blocks counteract the process of pontiprobation..while omalean globes regulize the pressure"...


Post Extras: Print Post  Remind Me! Notify Moderator
Jump to top. Pages: 1

General Interest >> Science and Technology

Similar ThreadsPosterViewsRepliesLast post
* Scale and the 5th dimension...
( 1 2 all )
undergrounder 2,317 34 05/08/08 05:28 AM
by undergrounder
* Topological Geometrodynamics (TGD) trendalM 1,019 3 10/21/03 02:41 PM
by trendal
* The tenth dimension archenemy 509 2 08/22/07 12:02 PM
by deimya
* Imagining the Tenth Dimension (Flash)
( 1 2 all )
ivi 2,924 38 08/12/06 02:51 PM
by barfightlard
* Jussst got a New computer and want to setup my old Dell Dimension 8100 only to run PROTOOLS? PsillyNilly 638 9 02/03/05 11:01 PM
by PsillyNilly
* Random power-downs with Dell Dimension 8400 SoY 602 3 03/01/07 05:58 PM
by Newbie
* gentoo 1 - automan 0 || UPDATE: AUTOMAN WINS IN FINAL SECONDS automanM 988 11 05/01/05 12:37 AM
by automan
* tesla: anyone ever built a plasma ball or jacobs ladder? eric_the_red 3,390 18 04/23/03 04:46 AM
by atomikfunksoldier

Extra information
You cannot start new topics / You cannot reply to topics
HTML is disabled / BBCode is enabled
Moderator: Lana, trendal, automan
521 topic views. 0 members, 0 guests and 0 web crawlers are browsing this forum.
[ Toggle Favorite | Print Topic | Stats ]
Search this thread:
Mycohaus
Please support our sponsors.

Copyright 1997-2018 Mind Media. Some rights reserved.

Generated in 0.032 seconds spending 0.006 seconds on 19 queries.