Am 29.07.2013 03:26, schrieb Ken Pledger: > In article <email@example.com>, > Thomas Nordhaus <firstname.lastname@example.org> wrote: > >> Am 28.07.2013 23:01, schrieb Ken Pledger: >>> .... >>> That's all. It's a traditional method in old text-books 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 old-fashioned. 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.