Sphere Eversion

Date: 8/11/96 at 13:49:45
From: T.J. J Jenkins
Subject: Sphere Eversion

Dear Dr. Math:

I heard someone speak of a blind mathematician who proved how to 
mathematically turn a sphere inside out.  Now, I don't know if
this person knew what he was talking about or not, but it seems an 
interesting proposition.

So, how do you mathematically turn a sphere inside out?

Thank you very much for your kind patience...

T.J. Jenkins

Date: 8/12/96 at 13:31:53
From: Doctor Jodi
Subject: Re: (no subject)

Hi T.J.! I haven't heard of a blind mathematician who has shown how to 
turn a sphere inside out, but there's a great movie made by the 
Geometry Center:

  http://www.geom.uiuc.edu    

which illustrates and explains Bill Thurston's method for turning a 
sphere inside out. The movie is called "Outside In". If you can't get 
a copy, don't despair: there is also a web page with highlights from 
the movie at 

  http://www.geom.uiuc.edu/docs/outreach/oi/   

and an accompanying book. The page also mentions that Stephen Smale 
was the first person to demonstrate how to turn a sphere inside out; 
perhaps he was the blind mathematician you mention?

You can download the QT movie of a sphere eversion at 

  http://www.geom.uiuc.edu/docs/outreach/oi/evert.qt   

Good luck and let us know if you have any more questions!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/