On Tue, 22 Feb 2005, Stephen Osborn wrote:

Larry Lard wrote:
Stephen Osborn wrote:

John Rowland wrote:

"Stephen Osborn" wrote in message
...

However the contours on an OS map (and AFAIK isobars on a weather
chart) never touch let alone cross.

They can touch, but they can't cross.

Contours mark places of equal height. If two contours touch at any
one point then, de definito, they have to touch at *all* points, so
the two contours become one contour.

This is a correct argument that two contours _indicating the same
height_ must be coincident if they have at least one point in common;
however consider contours marking _different_ heights; these can
coincide on a non-empty set of points (eg along a vertical cliff)
without necessarily coinciding everywhere.

That is true for a _literally_ vertical cliff, which does not actually
occur in nature.

It might happen that there are no perfectly vertical cliffs, but i don't
think it's impossible in principle, so that doesn't matter.

Also, you do get cliffs like this:

---------/
/
cliff /
/
/
/
/-------
| sea
|

Which are a bit of a problem, as the altitude is discontinuous as you go
from left to right - it goes from X feet in the air to zero without there
being any intervening points.

tom

PS It's best not to put a "-- " before your reply; well-brought-up news
software will trim everything below that from a reply.

--
Destroy - kill all hippies.