The Hofstadter point of a triangle 
is the perspector of
its 
-Hofstadter triangle and 
. The triangle
center function is
 |
(1)
|
The limiting Hofstadter point as 
has triangle
center function
 |
(2)
|
and is Kimberling center 
. The limiting Hofstadter point as 
has triangle
center function
 |
(3)
|
and is Kimberling center 
. These limits are taken in homogeneous trilinear
coordinates. 
and 
are examples of transcendental triangle centers,
since they have no trilinear coordinates
or barycentric coordinates using only
algebraic functions of the side
lengths 
,
, and 
.
