A Tale of Stern and Brocot

Here's a link to an interesting article on the tree
of Mr Stern's and Mr Brocot's independent efforts
from American Scientist. A short excerpt is below.

http://www.americanscientist.org/issues/Comsci00/compsci2000-07.html

There is no sign that either man knew of the other’s work. After the fact,
however, connections between them are easy to see; they are doing the same
thing but describing it differently.
There is even a connection between Brocot’s algorithm and the Fibonacci
series, where this whole quest began. To see the relation, just try using
Brocot’s method to find ratios approximating the constant known as phi, or
the golden ratio, an irrational number with a value of approximately 1.618.
The series of approximants begins 1/1, 2/1, 3/2, 5/3, 8/5, 13/8,.… Hidden
within these ratios is the complete sequence of Fibonacci numbers.

J Gill