A triple 
of positive integers satisfying 
is said to be geometric if 
. In particular, such a triple is geometric if its terms
form a geometric sequence with common
ratio 
where
 |
One can show that there exists a one-to-one correspondence between the set of equivalence
classes of geometric triples and the set of equivalence classes of harmonic
triples where here, two triples 
and 
are said to be equivalent
if 
,
i.e., if there exists some positive real
number 
such that 
.
