Thomas Nordhaus wrote: > 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.
The person who posted the problem may not mind how it's solved, but people are often interested in the most economical methods for what one might call aesthetic reasons.
-- Nam Nguyen in sci.logic in the thread 'Q on incompleteness proof' on 16/07/2013 at 02:16: "there can be such a group where informally it's impossible to know the truth value of the abelian expression Axy[x + y = y + x]".