For a nonzero real number 
and a triangle 
, swing line
segment 
about the vertex 
towards vertex 
through an angle 
. Call the line along the rotated segment 
. Construct a second line 
by rotating line segment 
about vertex 
through an angle 
. Now denote the point of intersection of 
and 
by 
. Similarly, construct 
and 
. The triangle having these
points as vertices is called the Hofstadter 
-triangle (Kimberling 1994; 1998, pp. 176-178 and 241-242).
For 
,
the resulting triangle is the first Morley triangle.
Kimberling (1994) showed that the Hofstadter triangle is perspective to 
, and calls perspective
center the Hofstadter point.
