
Re: Distance Between Lines in R^3 (fwd)
Posted:
Jul 29, 2013 2:16 AM


Am 29.07.2013 03:26, schrieb Ken Pledger: > In article <kt4635$fis$1@news.albasani.net>, > Thomas Nordhaus <thnord2002@yahoo.de> wrote: > >> Am 28.07.2013 23:01, schrieb Ken Pledger: >>> .... >>> That's all. It's a traditional method in old textbooks which aren't >>> read much any more, and it doesn't need any calculus. >> >> I think implicitly it does.... > > > It needs the fact that the shortest path from a point to a line is > along the perpendicular. My geometry students prove that as a little > exercise using Euclid I.16 and 19  definitely no calculus.
Now, THAT is oldfashioned. What is so wrong with using calculus? That way you can easily generalize to minimizing distance bewtween curves, submanifolds, whatever. I think there is nothing "old textbook"ish about it. That's simply differential geometry. You will find that outlined in Spivak's books.
> > Ken Pledger. >
 Thomas Nordhaus

