The 
-Hofstadter triangle of a given triangle 
is perspective to 
, and the perspector
is called the Hofstadter point. The triangle
center function is
 |
(1)
|
As 
,
the triangle center function approaches
 |
(2)
|
which is Kimberling center 
, and as 
, the triangle
center function approaches
 |
(3)
|
which is Kimberling center 
. 
and 
are examples of transcendental triangle centers, since
they have no trilinear or barycentric representation using only algebraic functions
of 
,
, and 
.
