FOM: Horn Angles and Non-standard Analysis

[Julio Gonzalez Cabillon]

\ Date: Fri, 7 Feb 1997 20:58:36 -0500
\ To: Jim Murdock <jmurdock at iastate.edu> 
\ From: Julio Gonzalez Cabillon <jgc at adinet.com.uy>
\ Subject: Re: horn angles
\ Cc: math-history-list at maa.org
\ 
\ Dear Jim,
\ 
\ At 12:11 AM 06/01/1997 -0500, you wrote:

| I have just read through (rather late) Julio's series of postings on horn 
| angles.  He ends with conformal mappings.  Bill's original question was 
| based on his research into pre-nonstandard analysis.  Which leaves the 
| question: does nonstandard analysis itself have anything to say about horn 
| angles?  Specifically: does any (or every) model of the nonstandard reals 
| contain an infinitesimal (unique? or not?) which can be assigned (for some 
| convincing reason) as the angle between a circle and its tangent?  Can this 
| perhaps be done via some of the infinitesimals that might be used in 
| nonstandard analysis in the course of defining the curvatures that appear 
| in the conformal approach?
| .....................................................................
| Jim Murdock                    "No matter how wrong things seem to be,
| Mathematics Dept.               they are still all right." 
| Iowa State University                                 -BW
| Ames Iowa 50011                   


\ Last year, before replying to Bill's original question, I was interested
\ in what non-standard analysis might add to the history of horn angles. 
\ I found NOTHING in the literature. Your non-standard analysis of my quick
\ survey seemed very interesting to me, though not music of the past.
\ 
\ Regards,
\          Julio

Further comments? JGC