Subject: Pits, peaks, passes (REVISED)
Date: Thu, 10 May 2001 17:24:47 +0100
From: Andrew Ranicki <aar@maths.ed.ac.uk>
To: Don Davis <dmd1@lehigh.edu>

%Dear Don
%There was a misprint in my previous message (destined for Hopf)
%Please use this version instead.
%Best wishes
%Andrew

The mountaineer's equation
pits - passes + peaks = 2
appeared in the 1870 paper "On Hills and Dales" by James Clerk Maxwell.
I have placed a scanned in copy on my website
http://www.maths.ed.ac.uk/~aar/surgery/hilldale.pdf
There is a wonderful account of the mountaineer's equation for a
general surface in Chapter 8 of H.B.Griffiths' book "Surfaces"
(Cambridge, 1976).
A Google search revealed that Maxwell's paper is actually used by
cartographers and computer visionaries:
http://citeseer.nj.nec.com/context/325476/0

Andrew Ranicki (Edinburgh)