FOM: Horn Angles and Non-standard Analysis
Julio Gonzalez Cabillon
jgc at adinet.com.uy
Wed Dec 3 10:54:36 EST 1997
\ 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.
Further comments? JGC
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