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
 |
There is a one-to-one correspondence between the set of equivalence
classes of geometric triples and the set
of equivalence classes of harmonic
triples satisfying 
and 
(VanderBurgh 2010, pp. 141-143). Here, two triples 
and 
belong to the same equivalence
class iff 
, i.e., if there exists some positive real
number 
such that 
.
