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Re: reason for "s = distance traveled"




On Sun, 24 Aug 1997 09:57:57 PST herbgottlieb@juno.com writes:

"Inge H. A. Pettersen" writes:
: "What is the reason for using >the letter s to denote distance
traveled ?".

The letter "d" is usually used for distance. For example , "A boy
walks 100 meters north and then 100 meters south. What is the total
distance that he walked?"

The letter "s" is usually used for displacement. Regardless of the
distance
that the boy walked, if he ends up at the same spot he started from,
his displacement is zero.

Herb Gottlieb from New York City
(Where we have many displaced persons from all over the world living
here)

Hi Herb, I think you might be misleading Inge here - besides not
answering his question, namely, why *small s*? I don't think we should
let anyone move us from our firm position in differential geometry with
(i) the Euclidean metric, ds = ... and (ii) arclength as a Riemann
integral given always the lower-case ess. Note the pictures of esses in
your dictionary. The Roman cursive minuscule really *is* the integral
sign, which is a sum of infinitesimals. Note, also, the look of the
sans serif late Latin majuscule. Doesn't that look just like the
stereotypical, nice, smooth, orientable, rectifiable curve in space?
Probably, that is not relevant. But, ds will be the element of length in
any metric, I'm pretty sure. This is a hard question. It may go back
to Newton, Leibnitz, or Gauss. And it may come from just about any
alphabet - from any language!

Hang in there, Inge.