Re: [Phys-l] zero width?

[John Denker <jsd@av8n.com>]

On 10/15/2007 11:30 AM, Rauber, Joel wrote:

> If you draw a line on the blackboard with chalk, the edge of the line
> has zero width.  I.e. its boundary


Yup, that's the idea.

Chalk is an excellent medium for this, because you can turn
the piece of chalk on its _side_ and make a nice fat mark.
This makes it obvious even to someone in the back of the
room that you are not trying to make a zero-width "line of
chalk".  You are making a region whereof the _boundary_ 
has zero width.

This scheme for representing something without width actually 
has some practical applications, for instance when the Secchi 
disk pattern is used as a fiducial on apparatus and on drawings 
of apparatus.
  http://www.av8n.com/physics/secchi-disk.htm

It's nice to be able to point to abstract ideas like this that
have practical applications.


It is also amusing to note that such boundaries are necessarily
_endless_.  This illustrates an important theorem from differential
topology, namely "the boundary of a boundary is zero".