A geometric triple is a triple 
of positive integers
satisfying 
for which 
.
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 
.
