On Jul 8, 6:17*pm, Giles wrote:
The question that arises is whether or not it's
worth the bother to pursue the closest approximation to a straight
line that is possible on a given route. *That is to say, over the
course of, say, a thousand mile cross-country trip, is there a
substantial savings in mileage and time to be gained by taking the
inside lane in each curve, switching lanes as necessary and taking the
shortest, straightest path possible between successive curves?

Don't know. *

In a similar vein, the old Rand McNally Road Atlas used to have (maybe
still does...) a great page in the back where it showed a few hundred
cities as dots, and had little red lines connecting them,
approximating the road networks. The lines were labeled with the
distance and time required to travel between these adjacent cities. In
my younger days I used to drive all over the place...a very similar
pattern to my older life it appears....and relied on this page a lot
for determining my route. I discovered that it was impossible to
determine the best route from LA to Boston, as there were only short
segments, but I assumed that if point C lay somewhere between point A
and point B, then the shortest distance from A to C, then C to B,
would be the shortest distance from A to C. Then, of course, add point
D between A and C, and point E between A and D, etc.....and strangely
enough...I soon found that the shortest distance from A to C worked
itself out from the details.

Seems obvious (and was later proven with mathematical studies of
Hamiltonian Paths and Euler Circuits and Dijkstra's Algorithm) but
you'd be suprised how many people will take the long (time and
distance) route around town on a highway rather than the short (time
and distance) route through town just because they are in love with
feeling motion. Travelling 60mph for a half hour seems like its
'faster' than travelling 30 mph for 25 minutes, yet people do it.

I think most people don't really think, let alone analyze, when they
are doing stuff. Its refreshing to hear stories of people who do.
You'd truly enjoy the opening chapter of "Beyond Numeracy' by John
Allen Paulos.

--riverman