**Navigational Mathematics**

There are excellent web resources on the history and the
mathematics of navigation. "The American Practical Navigator,"
first published by Nathaniel Bowditch in 1802, is entirely
downloadable from a site at Plymouth University,
which also has a page on Marine Navigation Calculations. Norris
Weimer at the University of Alberta has a page on
The
Mercator Conformal Projection with good historical links. Java applets
for calculating meridional parts and for solving the Mercator sailing
problem have been posted by Jacky Wong, webmaster of the Hong Kong
Marine Department.
## 1. How to get from here to there?

A standard problem in navigation is: given the coordinates
of two points on the earth's surface, to calculate how far and
in what direction one should travel to get from one to the
other.
Suppose we are traveling by air, or that the two points are on the
same body of water with no obstacles in the way. This makes it a
purely geometric problem.

There are in fact two traditional solutions to this problem.
One sets the course along the
the rhumb-line, the other along the great circle. "Mercator sailing" and
"Great circle sailing" are the names for the two kinds of
calculations involved. In this column
we will describe the two solutions and explain how they are
related.

--*Tony Phillips*

SUNY at Stony Brook

*Comments: webmaster@ams.org
*

© copyright 2000, American Mathematical Society.