  A Pythagorean triple is a triple of positive integers $(x,y,z)$ such that
$x^2+y^2=z^2$. If $x,y$ are coprime and $x$ is odd, then it is called a
primitive Pythagorean triple. Berggren showed that every primitive Pythagorean
triple can be generated from triple $(3,4,5)$ using multiplication by uniquely
number and order of three $3\times3$ matrices, which yields a ternary tree of
triplets. In this paper, we present some metric properties of triples in
Berggren tree. Firstly, we consider primitive Pythagorean triple as lengths of
sides of right triangles and secondly, we consider them as coordinates of
points in three-dimensional space.
